Geer, Gerard van der
Overview
Works:  42 works in 181 publications in 1 language and 2,890 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA573, 512.7 
Publication Timeline
.
Most widely held works by
Gerard van der Geer
Hilbert modular surfaces by
Gerard van der Geer(
Book
)
18 editions published between 1987 and 2012 in English and Undetermined and held by 391 WorldCat member libraries worldwide
Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples  in fact a whole chapter  completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field
18 editions published between 1987 and 2012 in English and Undetermined and held by 391 WorldCat member libraries worldwide
Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples  in fact a whole chapter  completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field
Introduction to coding theory and algebraic geometry by
Jacobus Hendricus van Lint(
Book
)
13 editions published in 1988 in English and held by 355 WorldCat member libraries worldwide
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 1621, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the GilbertVarshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI  CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
13 editions published in 1988 in English and held by 355 WorldCat member libraries worldwide
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 1621, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the GilbertVarshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI  CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Arithmetic algebraic geometry by
Gerard van der Geer(
Book
)
14 editions published in 1991 in English and Undetermined and held by 295 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 Undetermined and held by 295 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
The moduli space of curves by
R Dijkgraaf(
Book
)
10 editions published in 1995 in English and held by 286 WorldCat member libraries worldwide
The moduli space Mg of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteens conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory
10 editions published in 1995 in English and held by 286 WorldCat member libraries worldwide
The moduli space Mg of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteens conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory
Number fields and function fields : two parallel worlds by
Gerard van der Geer(
Book
)
24 editions published between 2005 and 2007 in English and held by 233 WorldCat member libraries worldwide
Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometricallyoriented world of function fields have led to new insights in the more arithmeticallyoriented world of number fields, or vice versa. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and tmotives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections. Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner
24 editions published between 2005 and 2007 in English and held by 233 WorldCat member libraries worldwide
Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometricallyoriented world of function fields have led to new insights in the more arithmeticallyoriented world of number fields, or vice versa. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and tmotives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections. Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner
Moduli of Abelian varieties by
C Faber(
Book
)
13 editions published in 2001 in English and held by 217 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
13 editions published in 2001 in English and held by 217 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
Lectures on Hilbert modular surfaces by
Friedrich Hirzebruch(
Book
)
10 editions published in 1981 in English and Undetermined and held by 180 WorldCat member libraries worldwide
10 editions published in 1981 in English and Undetermined and held by 180 WorldCat member libraries worldwide
Modular forms on schiermonnikoog by
B Edixhoven(
Book
)
12 editions published between 2004 and 2008 in English and held by 127 WorldCat member libraries worldwide
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspiration for Langlands' conjectures and play an important role in the description of the cohomology of varieties defined over number fields. This collection of uptodate articles originated from the conference 'Modular Forms' held on the Island of Schiermonnikoog in the Netherlands. A broad range of topics is covered including Hilbert and Siegel modular forms, Weil representations, Tannakian categories and Torelli's theorem. This book is a good source for all researchers and graduate students working on modular forms or related areas of number theory and algebraic geometry
12 editions published between 2004 and 2008 in English and held by 127 WorldCat member libraries worldwide
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspiration for Langlands' conjectures and play an important role in the description of the cohomology of varieties defined over number fields. This collection of uptodate articles originated from the conference 'Modular Forms' held on the Island of Schiermonnikoog in the Netherlands. A broad range of topics is covered including Hilbert and Siegel modular forms, Weil representations, Tannakian categories and Torelli's theorem. This book is a good source for all researchers and graduate students working on modular forms or related areas of number theory and algebraic geometry
Classification of algebraic varieties by Conference "Classification of Algebraic Varieties"(
Book
)
9 editions published in 2011 in English and held by 98 WorldCat member libraries worldwide
9 editions published in 2011 in English and held by 98 WorldCat member libraries worldwide
On Hilbert modular surfaces of principal congruence subgroups by
Gerard van der Geer(
Book
)
5 editions published between 1950 and 1977 in English and Undetermined and held by 18 WorldCat member libraries worldwide
5 editions published between 1950 and 1977 in English and Undetermined and held by 18 WorldCat member libraries worldwide
The moduli space of abelian varieties and the singularities of the theta divisor by
C Ciliberto(
Book
)
3 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
Supersingular curves of genus 2 over finite fields of characteristic 2 by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Kloosterman sums and the ptorsion of certain Jacobians by
Gerard van der Geer(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
On generalized Hamming weights of BCHcodes by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
On the existence of supersingular curves of given genus by
Gerard van der Geer(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Fibre products of artinschreier curves and generalized hamming weight of codes by
Gerard van der Geer(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
The 123 of modular forms : lectures at a summer school in Nordfjordeid, Norway by
Jan H Bruinier(
Book
)
5 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
This book grew out of three series of lectures given at the summer school on 'Modular Forms and their Applications' held in Nordfjordeid in June 2004
5 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
This book grew out of three series of lectures given at the summer school on 'Modular Forms and their Applications' held in Nordfjordeid in June 2004
Kodierungstheorie 30.04.  06.05.2000 by
Gerard van der Geer(
Book
)
1 edition published in 2000 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 3 WorldCat member libraries worldwide
Curves over finite fields of characteristic two with many rational points by
Gerard van der Geer(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we construct curves over finite fields in characteristic 2 with many rational points. The methods of construction are inspired by considerations from coding theory."
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we construct curves over finite fields in characteristic 2 with many rational points. The methods of construction are inspired by considerations from coding theory."
The second generalized Hamming weight of the dual codes of doubleerror correcting binary BCHcodes by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerrorcorrecting BCHcodes."
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerrorcorrecting BCHcodes."
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Related Identities
 Moonen, Ben Editor
 Faber, C. (Carel) 1962 Other Author Editor
 Oort, Frans 1935 Other Editor
 Lint, Jacobus Hendricus van 1932 Author
 Schoof, René
 Steenbrink, J. H. M. Editor
 Dijkgraaf, R. Other Editor
 Schoof, René Editor
 Edixhoven, B. (Bas) 1962 Author Editor
 Hirzebruch, Friedrich Author
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Associated Subjects
Abelian varieties Algebra Algebraic fields Algebraic topology Algebraic varietiesClassification theory Arithmetical algebraic geometry Coding theory Curves, Algebraic Errorcorrecting codes (Information theory) Finite fields (Algebra) Forms, Modular Geometry, Algebraic Hilbert modular surfaces Isomorphisms (Mathematics) Jacobi sums Kloosterman sums Mathematical physics Mathematics Moduli theory Number theory Physics Surfaces, Algebraic Topology
Alternative Names
De Geer, Gerard
Der Geer Gerard van
Geer, G. van der
Geer, G. van der 1950
Geer, G. van der (Gerard van der)
Geer, Gerardus Bartholomeus Maria van der
Geer, Gerardus Bartholomeus Maria van der 1950
Gerard van der Geer niederländischer Mathematikhistoriker
Van der Geer Gerard
Van der Geer, Gerard 1950
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