Bogomolov, Fedor 1946
Overview
Works:  47 works in 127 publications in 2 languages and 2,194 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor 
Classifications:  QA155, 512 
Publication Timeline
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Most widely held works by
Fedor Bogomolov
Geometric methods in algebra and number theory by
Fedor Bogomolov(
Book
)
20 editions published in 2005 in English and held by 272 WorldCat member libraries worldwide
"This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory. The collection gives a representative sample of problems and the most recent results in algebraic and arithmetic geometry; the text can serve as an intense introduction for graduate students and those wishing to pursue research in these areas."Résumé de l'éditeur
20 editions published in 2005 in English and held by 272 WorldCat member libraries worldwide
"This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory. The collection gives a representative sample of problems and the most recent results in algebraic and arithmetic geometry; the text can serve as an intense introduction for graduate students and those wishing to pursue research in these areas."Résumé de l'éditeur
Algebraic curves and onedimensional fields by
Fedor Bogomolov(
Book
)
9 editions published in 2002 in English and Undetermined and held by 235 WorldCat member libraries worldwide
Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out aspects of curves that are unique to them and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the RiemannRoch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear an
9 editions published in 2002 in English and Undetermined and held by 235 WorldCat member libraries worldwide
Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out aspects of curves that are unique to them and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the RiemannRoch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear an
Cohomological and geometric approaches to rationality problems : new perspectives by
Fedor Bogomolov(
Book
)
17 editions published in 2010 in English and held by 146 WorldCat member libraries worldwide
"This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality of moduli spaces of curves, and rational points on algebraic varieties. This volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems."Jacket
17 editions published in 2010 in English and held by 146 WorldCat member libraries worldwide
"This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality of moduli spaces of curves, and rational points on algebraic varieties. This volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems."Jacket
International Press Conference on Motives, Polylogarithms and Hodge Theory : University of California, Irvine, June 1998 by Polylogarithms and Hodge Theory International Press Conference on Motives(
Book
)
4 editions published in 2002 in English and held by 49 WorldCat member libraries worldwide
The present volume contains papers of the participants in the International Press Conference on Motives, polylogarithms and nonabelian Hodge theory which took place at UC Irvine in June 1998. The conference commemorated The twentieth anniversary of the remarkable Irvine lectures of Spencer Bloch on "Higher regulators, algebraic Ktheory and zeta functions of elliptic curves". The conference presented some of the best recent research in algebraic Ktheory, Hodge theory, motivic cohomology and polylogarithms. The research program of the conference was organized around three main lecture series: VladimirVoevodsky taught a minicourse overviewing the recent developments in motivic cohomology and motivic homotopy theory; Don Zagier lectured on new results describing the periods of holomorphic and nonholomorphic modular forms; and Carlos Simpson lectured on the theory of geometric nstacks and its applications to the variational aspects of nonabelian Hodge theory
4 editions published in 2002 in English and held by 49 WorldCat member libraries worldwide
The present volume contains papers of the participants in the International Press Conference on Motives, polylogarithms and nonabelian Hodge theory which took place at UC Irvine in June 1998. The conference commemorated The twentieth anniversary of the remarkable Irvine lectures of Spencer Bloch on "Higher regulators, algebraic Ktheory and zeta functions of elliptic curves". The conference presented some of the best recent research in algebraic Ktheory, Hodge theory, motivic cohomology and polylogarithms. The research program of the conference was organized around three main lecture series: VladimirVoevodsky taught a minicourse overviewing the recent developments in motivic cohomology and motivic homotopy theory; Don Zagier lectured on new results describing the periods of holomorphic and nonholomorphic modular forms; and Carlos Simpson lectured on the theory of geometric nstacks and its applications to the variational aspects of nonabelian Hodge theory
Birational geometry, rational curves, and arithmetic by
Fedor Bogomolov(
Book
)
12 editions published in 2013 in English and held by 30 WorldCat member libraries worldwide
¿¿¿¿This book features recent developments in a rapidly growing area at the interface of higherdimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic p
12 editions published in 2013 in English and held by 30 WorldCat member libraries worldwide
¿¿¿¿This book features recent developments in a rapidly growing area at the interface of higherdimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic p
Vector bundles by
Andrej Tyurin(
Book
)
1 edition published in 2008 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 9 WorldCat member libraries worldwide
International Press Conference on Motives, Polylogarithms and Hodge Theory : (University of California, Irvine, June 1998) by
Polylogarithms and Hodge Theory (1998, Irvine, Calif.) Conference on Motives(
Book
)
5 editions published in 2002 in English and held by 9 WorldCat member libraries worldwide
5 editions published in 2002 in English and held by 9 WorldCat member libraries worldwide
Geometric Methods in Algebra and Number Theory by
Fedor Bogomolov(
Book
)
1 edition published in 2006 in English and held by 8 WorldCat member libraries worldwide
The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory. Key topics include: Curves and their Jacobians Algebraic surfaceModuli spaces, Shimura varieties Motives and motivic integration Numberthe
1 edition published in 2006 in English and held by 8 WorldCat member libraries worldwide
The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory. Key topics include: Curves and their Jacobians Algebraic surfaceModuli spaces, Shimura varieties Motives and motivic integration Numberthe
Elliptic fibrations with fixed monodromy by
Tihomir Petrov(
)
1 edition published in 2002 in English and held by 6 WorldCat member libraries worldwide
We study moduli spaces of smooth nonisotrivial Jacobian elliptic fibrations over curves p:E & rarr;C with fixed global monodromy group G & d5;=G & d5; E & sub;SL 2Z . Let F be an irreducible algebraic family of Jacobian elliptic surfaces. Then the set of subgroups G & d5; & sub; SL2Z such that G & d5; is the (global) monodromy group of some E in this family is finite. Moreover, for every such group G & d5; the subset of fibrations with this monodromy of FG & d5; := & cubl0;p & isin;F & vbm0; G & d5; & parl0;E p & parr0;=G & d5; & cubr0; is an algebraic (not necessarily closed) subvariety of F
1 edition published in 2002 in English and held by 6 WorldCat member libraries worldwide
We study moduli spaces of smooth nonisotrivial Jacobian elliptic fibrations over curves p:E & rarr;C with fixed global monodromy group G & d5;=G & d5; E & sub;SL 2Z . Let F be an irreducible algebraic family of Jacobian elliptic surfaces. Then the set of subgroups G & d5; & sub; SL2Z such that G & d5; is the (global) monodromy group of some E in this family is finite. Moreover, for every such group G & d5; the subset of fibrations with this monodromy of FG & d5; := & cubl0;p & isin;F & vbm0; G & d5; & parl0;E p & parr0;=G & d5; & cubr0; is an algebraic (not necessarily closed) subvariety of F
Distribution of rational points on algebraic varieties by Sho Tanimoto(
)
1 edition published in 2012 in English and held by 6 WorldCat member libraries worldwide
We study the asymptotic formulas for the number of rational points of bounded height on equivariant compactications of solvable linear algebraic groups over a number field, and we introduce the notion of balanced line bundles
1 edition published in 2012 in English and held by 6 WorldCat member libraries worldwide
We study the asymptotic formulas for the number of rational points of bounded height on equivariant compactications of solvable linear algebraic groups over a number field, and we introduce the notion of balanced line bundles
On the cotangent bundle of a projective variety by Paolo Cascini(
)
1 edition published in 2004 in English and held by 6 WorldCat member libraries worldwide
For any smooth projective variety, we study a birational invariant, defined earlier on by Campana, depending on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We show how such invariant is related with other geometrical properties (as the fundamental group) and we describe new bounds for any projective variety of nonnegative Kodaira dimension
1 edition published in 2004 in English and held by 6 WorldCat member libraries worldwide
For any smooth projective variety, we study a birational invariant, defined earlier on by Campana, depending on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We show how such invariant is related with other geometrical properties (as the fundamental group) and we describe new bounds for any projective variety of nonnegative Kodaira dimension
Unramified Brauer groups of finite simple groups of Lie type Al by Jorge Arturo Maciel(
)
1 edition published in 2001 in English and held by 6 WorldCat member libraries worldwide
The cohomology theory of groups provides a way to obtain the ArtinMumford birational invariant for a smooth compactification of a quotient space V by the action of a linear algebraic group G. This invariant distinguishes the quotient spaces V/G from rational varieties. There are numerous finite groups for which this invariant is nonzero and thus the corresponding quotient varieties V/ G are not rational nor even stably rational. As a consequence of our main result we prove that the first obstruction to stable rationality is trivial for quotient spaces V/G where G is a finite simple group of Lie type Al
1 edition published in 2001 in English and held by 6 WorldCat member libraries worldwide
The cohomology theory of groups provides a way to obtain the ArtinMumford birational invariant for a smooth compactification of a quotient space V by the action of a linear algebraic group G. This invariant distinguishes the quotient spaces V/G from rational varieties. There are numerous finite groups for which this invariant is nonzero and thus the corresponding quotient varieties V/ G are not rational nor even stably rational. As a consequence of our main result we prove that the first obstruction to stable rationality is trivial for quotient spaces V/G where G is a finite simple group of Lie type Al
Torellitype theorem for curves defined over finite fields by Michael B Korotiaev(
)
1 edition published in 2007 in English and held by 6 WorldCat member libraries worldwide
The thesis studies Torellitype results for curves defined over finite fields. It is wellknown that under the standard embedding of the curve into its Jacobian, geometric points of the curve defined over a finite field generate the abstract torsion group of the geometric points of its Jacobian over an algebraic closure of a finite base field. In this work we ask to which extent the distribution of points on the curve inside the group of points on the Jacobian characterises the curve. Namely, we want to know what one can say about two curves of the same genus, whose settheoretic images under their respective Jacobian embeddings coincide (can be mapped in a onetoone and onto fashion by a group isomorphism of the torsiongroups of the geometric points of the Jacobians)
1 edition published in 2007 in English and held by 6 WorldCat member libraries worldwide
The thesis studies Torellitype results for curves defined over finite fields. It is wellknown that under the standard embedding of the curve into its Jacobian, geometric points of the curve defined over a finite field generate the abstract torsion group of the geometric points of its Jacobian over an algebraic closure of a finite base field. In this work we ask to which extent the distribution of points on the curve inside the group of points on the Jacobian characterises the curve. Namely, we want to know what one can say about two curves of the same genus, whose settheoretic images under their respective Jacobian embeddings coincide (can be mapped in a onetoone and onto fashion by a group isomorphism of the torsiongroups of the geometric points of the Jacobians)
On the fillability of contact structures on three dimensional manifolds by
F. A Bogomolov(
Book
)
4 editions published in 1993 in English and German and held by 5 WorldCat member libraries worldwide
4 editions published in 1993 in English and German and held by 5 WorldCat member libraries worldwide
Stein small deformations of strictly pseudoconvex surfaces by
Fedor Bogomolov(
Book
)
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Abstract: "This article analyses the behaviour of analytic cycles on deformations of strictly pseudoconvex surfaces. As a preliminary result we show that a relatively compact strictly pseudoconvex surface is the union of two Stein open subsets. The main result of the article is that there is a small deformation of a minimal relatively compact strictly pseudoconvex surface that has no positive dimensional analytic cycles, hence is Stein. We also prove that a strictly pseudoconvex surface contains a semiregular 1dimensional cycle if it contains one 1dim cycle. In the last section the main result is applied to the study of contact structures of three dimensional manifolds."
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Abstract: "This article analyses the behaviour of analytic cycles on deformations of strictly pseudoconvex surfaces. As a preliminary result we show that a relatively compact strictly pseudoconvex surface is the union of two Stein open subsets. The main result of the article is that there is a small deformation of a minimal relatively compact strictly pseudoconvex surface that has no positive dimensional analytic cycles, hence is Stein. We also prove that a strictly pseudoconvex surface contains a semiregular 1dimensional cycle if it contains one 1dim cycle. In the last section the main result is applied to the study of contact structures of three dimensional manifolds."
Rational curves and points on K3 surfaces by
Fedor Bogomolov(
Book
)
3 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
Fundamental groups in geometry : September 8th  September 14th, 2002(
Book
)
1 edition published in 2002 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 4 WorldCat member libraries worldwide
Complex projective surfaces and infinite groups by
Fedor Bogomolov(
Book
)
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
GEOMETRY OVER NONCLOSED FIELDS by
FEDOR BOGOMOLOV(
Book
)
5 editions published in 2017 in English and German and held by 4 WorldCat member libraries worldwide
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higherdimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higherdimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of longstanding conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
5 editions published in 2017 in English and German and held by 4 WorldCat member libraries worldwide
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higherdimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higherdimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of longstanding conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
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Related Identities
 Tschinkel, Yuri Editor
 Hassett, Brendan Editor
 Petrov, Tihomir Other Author
 Katzarkov, Ludmil 1961 Editor
 Conference on Motives, Polylogarithms and Hodge Theory (1998, Irvine, Calif.)
 Tyurin, Andrej Author
 Springer International Publishing AG Publisher
 Cappell, Sylvain
 Greenleaf, Frederick P.
 Cascini, Paolo Author
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Associated Subjects
Algebra Algebraic fields Convex surfaces Curves, Algebraic Fundamental groups (Mathematics) Geometry Geometry, Algebraic Group theory Hodge theory Homology theory Logarithmic functions Manifolds (Mathematics) Mathematics Motives (Mathematics) Number theory Projective curves Rational points (Geometry) Smooth affine curves Stein manifolds Surfaces, Algebraic Surfaces, Deformation of Topological groups Vector bundles
Alternative Names
Bogomolov, F. 1946
Bogomolov, F. A. 1946
Bogomolov, F. A. (Fedor A.), 1946
Bogomolov, Fedor 1946
Bogomolov, Fedor A.
Fedor Bogomolov matemático ruso
Fedor Bogomolov mathématicien russe
Fedor Bogomolov Russian mathematician
Fedor Bogomolov Russisch wiskundige
Fjodor Alexejewitsch Bogomolow russischer Mathematiker
Fjodor Bogomolov
Фёдор Алексеевич Богомолов
フョードル・ボゴモロフ
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