Oort, Frans 1935
Overview
Works:  79 works in 219 publications in 5 languages and 2,600 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Other, Correspondent 
Classifications:  QA564, 512.86 
Publication Timeline
.
Most widely held works by
Frans Oort
Commutative group schemes by
Frans Oort(
Book
)
30 editions published in 1966 in 4 languages and held by 464 WorldCat member libraries worldwide
We restrict ourselves to two aspects of the field of group schemes, in which the results are fairly complete: commutative algebraic group schemes over an algebraically closed field (of characteristic different from zero), and a duality theory concern{u00AD} ing abelian schemes over a locally noetherian prescheme. The prelim{u00AD} inaries for these considerations are brought together in chapter I. SERRE described properties of the category of commutative quasialgebraic groups by introducing proalgebraic groups. In char8teristic zero the situation is clear. In characteristic different from zero information on finite group schemee is needed in order to handle group schemes; this information can be found in work of GABRIEL. In the second chapter these ideas of SERRE and GABRIEL are put together. Also extension groups of elementary group schemes are determined. A suggestion in a paper by MANIN gave crystallization to a fee11ng of symmetry concerning subgroups of abelian varieties. In the third chapter we prove that the dual of an abelian scheme and the linear dual of a finite subgroup scheme are related in a very natural way. Afterwards we became aware that a special case of this theorem was already known by CARTIER and BARSOTTI. Applications of this duality theorem are: the classical duality theorem ("duality hy{u00AD} pothesis", proved by CARTIER and by NISHI); calculation of Ext(ã, A), where A is an abelian variety (result conjectured by SERRE); a proof of the symmetry condition (due to MANIN) concerning the isogeny type of a formal group attached to an abelian variety
30 editions published in 1966 in 4 languages and held by 464 WorldCat member libraries worldwide
We restrict ourselves to two aspects of the field of group schemes, in which the results are fairly complete: commutative algebraic group schemes over an algebraically closed field (of characteristic different from zero), and a duality theory concern{u00AD} ing abelian schemes over a locally noetherian prescheme. The prelim{u00AD} inaries for these considerations are brought together in chapter I. SERRE described properties of the category of commutative quasialgebraic groups by introducing proalgebraic groups. In char8teristic zero the situation is clear. In characteristic different from zero information on finite group schemee is needed in order to handle group schemes; this information can be found in work of GABRIEL. In the second chapter these ideas of SERRE and GABRIEL are put together. Also extension groups of elementary group schemes are determined. A suggestion in a paper by MANIN gave crystallization to a fee11ng of symmetry concerning subgroups of abelian varieties. In the third chapter we prove that the dual of an abelian scheme and the linear dual of a finite subgroup scheme are related in a very natural way. Afterwards we became aware that a special case of this theorem was already known by CARTIER and BARSOTTI. Applications of this duality theorem are: the classical duality theorem ("duality hy{u00AD} pothesis", proved by CARTIER and by NISHI); calculation of Ext(ã, A), where A is an abelian variety (result conjectured by SERRE); a proof of the symmetry condition (due to MANIN) concerning the isogeny type of a formal group attached to an abelian variety
Algebraic geometry, Oslo 1970; proceedings by
Frans Oort(
Book
)
23 editions published in 1972 in English and Undetermined and held by 329 WorldCat member libraries worldwide
23 editions published in 1972 in English and Undetermined and held by 329 WorldCat member libraries worldwide
Moduli of supersingular abelian varieties by
KeZheng Li(
Book
)
18 editions published in 1998 in English and held by 316 WorldCat member libraries worldwide
Content Description #Includes bibliographical references and index
18 editions published in 1998 in English and held by 316 WorldCat member libraries worldwide
Content Description #Includes bibliographical references and index
Arithmetic algebraic geometry by
J Oesterlé(
Book
)
14 editions published in 1991 in English and held by 289 WorldCat member libraries worldwide
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin's work, Ktheory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the BirchSwinnertonDyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this stateoftheart selection
14 editions published in 1991 in English and held by 289 WorldCat member libraries worldwide
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin's work, Ktheory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the BirchSwinnertonDyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this stateoftheart selection
Moduli of Abelian varieties by
C Faber(
Book
)
14 editions published in 2001 in English and held by 220 WorldCat member libraries worldwide
Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics
14 editions published in 2001 in English and held by 220 WorldCat member libraries worldwide
Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics
Complex multiplication and lifting problems by
ChingLi Chai(
Book
)
7 editions published in 2014 in English and held by 206 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
7 editions published in 2014 in English and held by 206 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
Reducible and multiple algebraic curves by
Frans Oort(
Book
)
10 editions published in 1961 in English and held by 57 WorldCat member libraries worldwide
10 editions published in 1961 in English and held by 57 WorldCat member libraries worldwide
The legacy of Bernhard Riemann after one hundred and fifty years(
Book
)
1 edition published in 2016 in English and held by 26 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 26 WorldCat member libraries worldwide
Resolution of singularities : a research textbook in tribute to Oscar Zariski : based on the courses given at the working
week in Obergurgl, Austria, September 714, 1997 by
H Hauser(
Book
)
6 editions published in 2000 in English and held by 24 WorldCat member libraries worldwide
In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems
6 editions published in 2000 in English and held by 24 WorldCat member libraries worldwide
In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems
Representations des groupes lineaires by
Peter Gabriel(
Book
)
7 editions published in 1970 in 3 languages and held by 20 WorldCat member libraries worldwide
7 editions published in 1970 in 3 languages and held by 20 WorldCat member libraries worldwide
Vraagstukken over lineaire algebra by
Johan Christoph Boland(
Book
)
5 editions published between 1965 and 1970 in Dutch and held by 16 WorldCat member libraries worldwide
5 editions published between 1965 and 1970 in Dutch and held by 16 WorldCat member libraries worldwide
The Legacy of Bernhard Riemann after one hundred and fifty years. companion to the volume The Legacy of Bernhard Riemann after
one hundred and fifty years, volume I(
Book
)
4 editions published in 2016 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2016 in English and held by 9 WorldCat member libraries worldwide
Vlijt, visie, verificatie : aspecten van de wiskundebeoefening by
Frans Oort(
Book
)
4 editions published in 1968 in Dutch and held by 7 WorldCat member libraries worldwide
4 editions published in 1968 in Dutch and held by 7 WorldCat member libraries worldwide
Algebra of meetkunde? by
Frans Oort(
Book
)
1 edition published in 1964 in Dutch and held by 6 WorldCat member libraries worldwide
1 edition published in 1964 in Dutch and held by 6 WorldCat member libraries worldwide
Een pak met een korte broek by
P. van Emde Boas(
Book
)
1 edition published in 1977 in Dutch and held by 6 WorldCat member libraries worldwide
1 edition published in 1977 in Dutch and held by 6 WorldCat member libraries worldwide
Fine and coarse moduli schemes are different by
Frans Oort(
Book
)
2 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Lectures on homotopy theory and half exact functors by
A Dold(
Book
)
3 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
Which abelian surfaces are products of elliptic curves? by
Frans Oort(
Book
)
2 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
Galoistheorie by
H. W Lenstra(
Book
)
1 edition published in 1972 in Dutch and held by 4 WorldCat member libraries worldwide
1 edition published in 1972 in Dutch and held by 4 WorldCat member libraries worldwide
Syllabus commutatieve algebra by
Frans Oort(
Book
)
1 edition published in 1973 in Dutch and held by 3 WorldCat member libraries worldwide
1 edition published in 1973 in Dutch and held by 3 WorldCat member libraries worldwide
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Related Identities
 Geer, Gerard van der Other Author Editor
 Li, KeZheng 1949 Author
 Steenbrink, J. H. M. Editor
 Faber, C. (Carel) 1962 Other Author Editor
 Nordic Council of Ministers Nordiska kulturkommissionen
 Conrad, Brian 1970
 Chai, ChingLi Author
 Lipman, Joseph Editor
 Hauser, Herwig Author Editor
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Associated Subjects
Abelian groups Abelian varieties Algebra Algebraic varietiesClassification theory Algebras, Linear Arithmetical algebraic geometry Curves, Algebraic Functor theory Geometry, Algebraic Group schemes (Mathematics) Homotopy theory Linear algebraic groups Mathematics MathematicsPhilosophy Moduli theory Multiplication, Complex Number theory Riemann, Bernhard, Riemann hypothesis Riemann surfaces Singularities (Mathematics)
Alternative Names
Frans Oort Dutch mathematician
Frans Oort Nederlands wiskundige
Frans Oort nederlandsk matematikar
Frans Oort nederländsk matematiker
Frans Oort niederländischer Mathematiker
Oort, F.
Oort, F. 1935
Oort, F. (Frans), 1935
Oort, Frans
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