Conrad, Brian 1970Overview
Most widely held works by
Brian Conrad
Grothendieck duality and base change
by Brian Conrad
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Book
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21 editions published between 2000 and 2002 in English and held by 463 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
Pseudoreductive groups
by Brian Conrad
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Book
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13 editions published between 2010 and 2015 in English and Undetermined and held by 242 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 selfcontained monograph provides a comprehensive treatment of the theory of pseudoreductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudoparabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, 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"
Arithmetic algebraic geometry
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Book
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9 editions published between 2001 and 2008 in English and held by 231 WorldCat member libraries worldwide
Complex multiplication and lifting problems
by ChingLi Chai
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Book
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4 editions published in 2014 in English and held by 180 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
Modular forms and the Ramanujan Conjecture
by Brian Conrad
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Book
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1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
Rocky mountain tales : wit and wisdom of the wild West
by Arlene Pervin
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Book
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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
The Weil conjectures for curves
by Brian Conrad
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1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
Algebraic modular forms on definite orthogonal groups
by Daniel Kim Murphy
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1 edition published in 2013 in English and held by 1 WorldCat member library worldwide The present thesis examines explicit computation with modular forms on definite orthogonal groups over the rational numbers. The space of functions on the genus of a definite quadratic form affords a natural representation of the Hecke algebra, which realizes the function space as a space of modular forms. The algorithm of the thesis computes the genus of a quadratic form as well as Hecke operators on the associated space of modular forms. A formula derived in the thesis yields Satake parameters from Hecke eigenvalues. Explicit examples of Satake parameters verify the correctness of the algorithm and the formula by their agreement with the predictions of the Arthur conjectures
Zerodistribution and size of the Riemann zetafunction on the critical line
by Maksym Radziwill
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1 edition published in 2013 in English and held by 1 WorldCat member library worldwide We investigate the analytic properties of the Riemann zetafunction. We focus on the average size of the Riemann zetafunction on the critical line and on the vertical distribution of its zeros on the critical line
Live!
by Jerry Frank Trio
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Recording
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1 edition published in 1981 and held by 1 WorldCat member library worldwide
Padic geometry : lectures from the 2007 Arizona Winter School
by Arizona Winter School
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Book
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1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Equivariant torsion and base change
by Michael Lipnowski
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1 edition published in 2013 in English and held by 1 WorldCat member library worldwide The CheegerMuller theorem provides a spectral means of obtaining information about torsion in the cohomology of compact manifolds. Using this remarkable theorem together with trace formula comparisons, we prove comparisons between torsion in the cohomology of two manifolds of arithmetic origin related by base change
General existence theorems in moduli theory
by Jack Kingsbury Hall
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1 edition published in 2011 in English and held by 1 WorldCat member library worldwide In this thesis, we prove that there is an algebraic stack parameterizing all curves. The curves that appear in this algebraic stack are allowed to be arbitrarily singular, nonreduced, disconnected, and reducible. We also prove the boundedness of the open substack parameterizing reduced and connected curves with fixed arithmetic genus g and at most e irreducible components. We also show that for essentially any algebraic stack, there is an algebraic stack, the Hilbert stack, parameterizing quasifinite maps to the stack. The technical heart of this result is a generalization of formal GAGA to a nonseparated morphism of algebraic stacks, something that was previously unknown for a morphism of schemes. We also employ derived algebraic geometry, in an essential way, to prove the algebraicity of the Hilbert stack. The Hilbert stack, for algebraic spaces, was claimed to exist by M. Artin (1974), but was left unproved due to a lack of foundational results for nonseparated algebraic spaces. Finally, we generalize the fundamental GAGA results of J.P. Serre (1956) in three waysto the nonseparated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of the moduli stack of smooth curves possessing modular interpretations are algebraizable
Gvalued flat deformations and local models
by Brandon William Allen Levin
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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
Moduli spaces of PTstable objects
by ChiehCheng Lo
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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
Some problems in multiplicative number theory
by Junsoo Ha
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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
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Book
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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
Padic Hodge theory in rigid analytic families
by Rebecca Michal Bellovin
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1 edition published in 2013 in English and held by 1 WorldCat member library worldwide In this thesis, we study padic Hodge theory in rigid analytic families. Roughly speaking, padic Hodge theory is the study of padic representations of padic Galois groups. One introduces certain padic period rings B, such as B_{HT}, B_{dR}, B_{st}, and B_{cris}, and uses them to define functors D_B(.) from the category of padic Galois representations to various categories of linear algebra data. In the first half of this thesis, we study generalizations of these functors to families of padic Galois representations with rigid analytic coefficients. We prove that the functors D_{HT}(.) and D_{dR}(.) are coherent sheaves, and we prove that the Badmissible locus is a closed subspace of the base. In the second half of this thesis, we study the linear algebra data which arises from families of potentially semistable Galois representations valued in a connected reductive group G. We prove that for any G, the moduli space of linear algebra data is reduced and locally a complete intersection, and we deduce that potentially semistable deformation rings are generically smooth and equidimensional
Finite Honda systems and supersingular elliptic curves
by Brian Conrad
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Book
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1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Controlling ramification in number fields
by Simon RubinsteinSalzedo
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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 more
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Abelian varieties Arithmetical algebraic geometry Artificial satellites in telecommunication CanadaCanadian Rockies Commercial leases Communications, Military Curves Duality theory (Mathematics) Folklore Forms, Modular Frontier and pioneer life Galois theory Geometry, Algebraic Grothendieck groups Group theory Jazz Lifting theory Linear algebraic groups Mathematics Military telecommunication Multiplication, Complex Number theory padic analysis Schemes (Algebraic geometry) United States Weil conjectures

Alternative Names
Conrad, B. 1970
Conrad, Brian.
Conrad, Brian David
Conrad, Brian David 1970
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