Conrad, Brian 1970
Overview
Works:  28 works in 76 publications in 2 languages and 1,276 library holdings 

Genres:  Conference proceedings Anecdotes History Biography 
Roles:  Author, Thesis advisor, Collector, Editor, Creator, Performer 
Classifications:  QA564, 512.74 
Publication Timeline
.
Most widely held works by
Brian Conrad
Grothendieck duality and base change by
Brian Conrad(
Book
)
21 editions published between 2000 and 2002 in English and held by 339 WorldCat member libraries worldwide
Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper CohenMacaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory
21 editions published between 2000 and 2002 in English and held by 339 WorldCat member libraries worldwide
Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper CohenMacaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory
Arithmetic algebraic geometry(
Book
)
9 editions published between 2001 and 2008 in English and held by 235 WorldCat member libraries worldwide
9 editions published between 2001 and 2008 in English and held by 235 WorldCat member libraries worldwide
Complex multiplication and lifting problems by
ChingLi Chai(
Book
)
6 editions published in 2014 in English and held by 198 WorldCat member libraries worldwide
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.  Provided by publisher
6 editions published in 2014 in English and held by 198 WorldCat member libraries worldwide
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.  Provided by publisher
Pseudoreductive groups by
Brian Conrad(
Book
)
16 editions published between 2010 and 2015 in English and Undetermined and held by 193 WorldCat member libraries worldwide
"Pseudoreductive groups arise naturally in the study of general smooth linear algebraic groups over nonperfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudoreductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasireductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudosplit absolutely pseudosimple groups with a nonreduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudoreductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems"
16 editions published between 2010 and 2015 in English and Undetermined and held by 193 WorldCat member libraries worldwide
"Pseudoreductive groups arise naturally in the study of general smooth linear algebraic groups over nonperfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudoreductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasireductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudosplit absolutely pseudosimple groups with a nonreduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudoreductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems"
Autour des schémas en groupes. group schemes, a celebration of SGA3(
Book
)
1 edition published in 2014 in French and held by 7 WorldCat member libraries worldwide
1 edition published in 2014 in French and held by 7 WorldCat member libraries worldwide
Estuarine bycatch assessment in NC commercial fisheries : report to National Marine Fisheries Service, Atlantic Coastal Cooperative
Statistics Program(
)
in English and held by 4 WorldCat member libraries worldwide
in English and held by 4 WorldCat member libraries worldwide
Rocky mountain tales : wit and wisdom of the wild West by
Arlene Pervin(
Book
)
1 edition published in 2010 in English and held by 4 WorldCat member libraries worldwide
" ... reveals what life was like in the West through humour, political satire, and comentary in the writing of legendary newspapermen who lived and wrote of their time and place and dared to cross the line, in words and their vision for the West" p. [4] of cover
1 edition published in 2010 in English and held by 4 WorldCat member libraries worldwide
" ... reveals what life was like in the West through humour, political satire, and comentary in the writing of legendary newspapermen who lived and wrote of their time and place and dared to cross the line, in words and their vision for the West" p. [4] of cover
Modular forms and the Ramanujan Conjecture by
Brian Conrad(
Book
)
1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
Autour des schémas en groupes : group schemes, a celebration of SGA3 by École d'été "Schémas en groupes"(
Book
)
in French and held by 3 WorldCat member libraries worldwide
Volume 1 "contains the first part of the lecture notes of the Summer school 'Group Schemes, introduction to the SGA3 seminar of DemazureGrothendieck,' which was held at the Centre International de Rencontres Mathématiques (CIRM) at Luminy in September 2011. This summer school was devoted to the theory of group schemes and especially of reductive group schemes. The contributions in this first part are expanded versions of the talks introducing Grothendieck topologies (S. Brochard), group schemes of multiplicative type (J. Oesterlé) and reductive group schemes (B. Conrad)."
in French and held by 3 WorldCat member libraries worldwide
Volume 1 "contains the first part of the lecture notes of the Summer school 'Group Schemes, introduction to the SGA3 seminar of DemazureGrothendieck,' which was held at the Centre International de Rencontres Mathématiques (CIRM) at Luminy in September 2011. This summer school was devoted to the theory of group schemes and especially of reductive group schemes. The contributions in this first part are expanded versions of the talks introducing Grothendieck topologies (S. Brochard), group schemes of multiplicative type (J. Oesterlé) and reductive group schemes (B. Conrad)."
Classification of pseudoreductive groups by
Brian Conrad(
Book
)
1 edition published in 2016 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 3 WorldCat member libraries worldwide
The Weil conjectures for curves by
Brian Conrad(
)
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
Controlling ramification in number fields by Simon RubinsteinSalzedo(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
This thesis focuses on two aspects of limited ramification and is split up into two independent sections. The first section (which comprises the second and third chapters) is on the distribution of class groups of cyclic cubic fields. We propose an explanation for the discrepancy between the observed number of cyclic cubics whose 2class group is C_2 x C_2 and the number predicted by the CohenLenstra heuristics, in terms of an invariant living in a quotient of the Schur multiplier group. We also show that, in some cases, the definition of the invariant can be simplified greatly, and we compute 10^5 examples. The second section (which comprises the fourth and fifth chapters) discusses branched covers of algebraic curves, especially covers of elliptic curves with one branch point. We produce some techniques that allow us to write down explicit equations for such maps, and then we give examples of number fields which arise from such covers. Finally, we present some possibilities for future works that the author hopes to pursue
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
This thesis focuses on two aspects of limited ramification and is split up into two independent sections. The first section (which comprises the second and third chapters) is on the distribution of class groups of cyclic cubic fields. We propose an explanation for the discrepancy between the observed number of cyclic cubics whose 2class group is C_2 x C_2 and the number predicted by the CohenLenstra heuristics, in terms of an invariant living in a quotient of the Schur multiplier group. We also show that, in some cases, the definition of the invariant can be simplified greatly, and we compute 10^5 examples. The second section (which comprises the fourth and fifth chapters) discusses branched covers of algebraic curves, especially covers of elliptic curves with one branch point. We produce some techniques that allow us to write down explicit equations for such maps, and then we give examples of number fields which arise from such covers. Finally, we present some possibilities for future works that the author hopes to pursue
Finite Honda systems and supersingular elliptic curves by
Brian Conrad(
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Some problems in multiplicative number theory by Junsoo Ha(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Let q be a power of a prime p. In the first part of this thesis, we establish the upper bound of the least prime primitive root mod q by p^3.1. We say a polynomial in F_q [T] is msmooth if all of its irreducible factors are of degree less than or equal to m. Let N(n, m) be the number of solutions to the polynomial equation X+Y=2Z where all variables are msmooth polynomials of degree n. In the second part of this thesis, we establish a lower bound on N(n, m) when (8+d) log_q n < = m < = n^1/2 for small d, and prove the analog of the xyz conjecture of Lagarias and Soundararajan in the polynomial rings over finite fields
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Let q be a power of a prime p. In the first part of this thesis, we establish the upper bound of the least prime primitive root mod q by p^3.1. We say a polynomial in F_q [T] is msmooth if all of its irreducible factors are of degree less than or equal to m. Let N(n, m) be the number of solutions to the polynomial equation X+Y=2Z where all variables are msmooth polynomials of degree n. In the second part of this thesis, we establish a lower bound on N(n, m) when (8+d) log_q n < = m < = n^1/2 for small d, and prove the analog of the xyz conjecture of Lagarias and Soundararajan in the polynomial rings over finite fields
A conceptual framework for tactical private satellite networks by
Brian Conrad(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
The purpose of this research is threefold. First is to examine the current state of military satellite communications and to analyze current trends in the commercial satellite communications market that support military Command and Control, as well as facilitate network operations. Second is the operational implementation of such private satellite networks within the context of Net Centric Operations, as well as within the context of a coalition environment. Third, this work will illustrate how the private satellite network could be managed, as well as understanding how the network could be used in the context of a network management control channel to exercise management of numerous dispersed network devices and nodes. The focus will be to define, examine, and research the conceptual framework for a tactical private satellite network that facilitates Command and Control of geographically dispersed tactical units, as well as provides a mechanism for the management of tactical networks. After having acquired a clear picture of today's state and future's capabilities of SATCOM, research will be directed to how a tactical private satellite network would be implemented to support Network Centric Operations and how this tactical private satellite network could be utilized as a tool for the management of tactical networks. During the research, a number of secondary, yet supportive topics, need to be examined, such as, how that tactical private satellite network can be implemented to facilitate collaboration between Other Government Agencies, NonGovernmental Organizations, and Coalition partners from other countries or how it would be managed to offer to its subscribers the desired service in terms of quantity (throughput) and overall quality. To materialize the above, this thesis considers it essential to thoroughly examine a commercial base station which is fully capable of managing this satellite network under any conditions. The whole concept of this Tactical Private Satellite Network is examined based on two innovative approaches. First, the establishment of two different logical channels inside the physical one and second, the concept of a private satellite network and its implementation is examined as a method for direct delivery of data
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
The purpose of this research is threefold. First is to examine the current state of military satellite communications and to analyze current trends in the commercial satellite communications market that support military Command and Control, as well as facilitate network operations. Second is the operational implementation of such private satellite networks within the context of Net Centric Operations, as well as within the context of a coalition environment. Third, this work will illustrate how the private satellite network could be managed, as well as understanding how the network could be used in the context of a network management control channel to exercise management of numerous dispersed network devices and nodes. The focus will be to define, examine, and research the conceptual framework for a tactical private satellite network that facilitates Command and Control of geographically dispersed tactical units, as well as provides a mechanism for the management of tactical networks. After having acquired a clear picture of today's state and future's capabilities of SATCOM, research will be directed to how a tactical private satellite network would be implemented to support Network Centric Operations and how this tactical private satellite network could be utilized as a tool for the management of tactical networks. During the research, a number of secondary, yet supportive topics, need to be examined, such as, how that tactical private satellite network can be implemented to facilitate collaboration between Other Government Agencies, NonGovernmental Organizations, and Coalition partners from other countries or how it would be managed to offer to its subscribers the desired service in terms of quantity (throughput) and overall quality. To materialize the above, this thesis considers it essential to thoroughly examine a commercial base station which is fully capable of managing this satellite network under any conditions. The whole concept of this Tactical Private Satellite Network is examined based on two innovative approaches. First, the establishment of two different logical channels inside the physical one and second, the concept of a private satellite network and its implementation is examined as a method for direct delivery of data
CM liftings by
ChingLi Chai(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Modular forms and Fermat's last theorem(
Book
)
in English and held by 1 WorldCat member library worldwide
"The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the LanglandsTunnell theorem, and this is followed by indepth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections, and more, as the reader is led stepbystep through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epochmaking proof of Fermat's Last Theorem."Jacket
in English and held by 1 WorldCat member library worldwide
"The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the LanglandsTunnell theorem, and this is followed by indepth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections, and more, as the reader is led stepbystep through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epochmaking proof of Fermat's Last Theorem."Jacket
Moduli spaces of PTstable objects by ChiehCheng Lo(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
We develop techniques for performing semistable reduction on a flat family of objects in the heart of a tstructure on the bounded derived category of coherent sheaves of a smooth projective threefold. Then we show that, with respect to Bayer's PTstability function, the semistable objects in the heart of perverse sheaves form a proper Artin stack of finite type, provided the rank is nonzero, and the rank and degree are coprime
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
We develop techniques for performing semistable reduction on a flat family of objects in the heart of a tstructure on the bounded derived category of coherent sheaves of a smooth projective threefold. Then we show that, with respect to Bayer's PTstability function, the semistable objects in the heart of perverse sheaves form a proper Artin stack of finite type, provided the rank is nonzero, and the rank and degree are coprime
Gvalued flat deformations and local models by Brandon William Allen Levin(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We construct resolutions of Gvalued local Galois deformation rings by moduli spaces of Kisin modules with Gstructure when l = p. This generalizes Mark Kisin's work on potentially semistable deformation rings. In the case of flat deformations, we prove a structural result about these resolutions which relates the connected components of Gvalued flat deformation rings to the connected components of projective varieties in characteristic p, which are moduli spaces of linear algebra data. As a key step in the study of these resolutions, we prove a full faithfulness result in integral padic Hodge theory. We also generalize results of Pappas and Zhu on local models of Shimura varieties to groups arising from Weil restrictions
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We construct resolutions of Gvalued local Galois deformation rings by moduli spaces of Kisin modules with Gstructure when l = p. This generalizes Mark Kisin's work on potentially semistable deformation rings. In the case of flat deformations, we prove a structural result about these resolutions which relates the connected components of Gvalued flat deformation rings to the connected components of projective varieties in characteristic p, which are moduli spaces of linear algebra data. As a key step in the study of these resolutions, we prove a full faithfulness result in integral padic Hodge theory. We also generalize results of Pappas and Zhu on local models of Shimura varieties to groups arising from Weil restrictions
Padic geometry : lectures from the 2007 Arizona Winter School by Arizona Winter School(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Prasad, Gopal
 Gabber, Ofer 1958
 Rubin, Karl Editor
 Chai, ChingLi Author
 Oort, Frans 1935
 SpringerLink (Service en ligne)
 Oesterlé, Joseph Collector
 Brochard, Sylvain (1979....). Collector
 Stanford University Department of Mathematics
 Venkatesh, Akshay 1981 Thesis advisor
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Associated Subjects
Abelian varieties Arithmetical algebraic geometry Artificial satellites in telecommunication CanadaCanadian Rockies Commercial leases Communications, Military Curves Curves, Elliptic Duality theory (Mathematics) Estuarine ecology Fermat's last theorem Fishery management Folklore Forms, Modular Frontier and pioneer life Galois theory Geometry, Algebraic Group schemes (Mathematics) Group theory Linear algebraic groups Mathematics Military telecommunication Multiplication, Complex North Carolina Number theory padic analysis Schemes (Algebraic geometry) Sustainable fisheries Topology United States Weil conjectures
Alternative Names
Brian Conrad Amerikaans wiskundige
Brian Conrad amerikansk matematikar
Brian Conrad amerikansk matematiker
Brian Conrad matematico americano
Brian Conrad mathmaticien amricain
Brian Conrad USamerikanischer Mathematiker
Conrad, B. 1970
Conrad, Brian.
Conrad, Brian David
Conrad, Brian David 1970
Брайан Конрад
برایان کنراد ریاضیدان آمریکایی
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