WorldCat Identities

Oort, Frans 1935-

Overview
Works: 80 works in 223 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
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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 463 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 ing abelian schemes over a locally noetherian prescheme. The prelim­ inaries for these considerations are brought together in chapter I. SERRE described properties of the category of commutative quasi-algebraic groups by introducing pro-algebraic 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 pothesis", proved by CARTIER and by NISHI); calculation of Ext(~a,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

Moduli of supersingular abelian varieties by Ke-Zheng Li( Book )

18 editions published in 1998 in English and held by 312 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 288 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, K-theory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the Birch-Swinnerton-Dyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection
Moduli of Abelian varieties by C Faber( Book )

14 editions published in 2001 in English and held by 219 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 Ching-Li Chai( Book )

7 editions published in 2014 in English and held by 208 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

The legacy of Bernhard Riemann after one hundred and fifty years( Book )

2 editions published in 2016 in English and held by 30 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 7-14, 1997 by H Hauser( Book )

6 editions published in 2000 in English and held by 25 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 )

6 editions published in 1970 in French and Dutch and held by 19 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 17 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

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

Algebra of meetkunde? by Frans Oort( Book )

1 edition published in 1964 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

Galoistheorie by H. W Lenstra( Book )

1 edition published in 1972 in Dutch and held by 4 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

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

Syllabus commutatieve algebra by Frans Oort( Book )

1 edition published in 1973 in Dutch and held by 3 WorldCat member libraries worldwide

 
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Algebraic geometry, Oslo 1970; proceedings
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

Languages
English (129)

Dutch (15)

French (4)

German (2)

Italian (1)

Covers
Algebraic geometry, Oslo 1970; proceedingsModuli of supersingular abelian varietiesArithmetic algebraic geometryModuli of Abelian varietiesResolution of singularities : a research textbook in tribute to Oscar Zariski : based on the courses given at the working week in Obergurgl, Austria, September 7-14, 1997