Author: T. Yamada
Publisher: Springer
ISBN: 3540377336
Category : Mathematics
Languages : en
Pages : 165
Book Description
The Schur Subgroup of the Brauer Group
Author: T. Yamada
Publisher: Springer
ISBN: 3540377336
Category : Mathematics
Languages : en
Pages : 165
Book Description
Publisher: Springer
ISBN: 3540377336
Category : Mathematics
Languages : en
Pages : 165
Book Description
Schur Subgroup of the Brauer Group
Author: Toshihiko Yamada
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Schur Subgroup of the Brauer Group
Author: James William Pendergrass
Publisher:
ISBN:
Category : Algebraic number theory
Languages : en
Pages : 232
Book Description
Publisher:
ISBN:
Category : Algebraic number theory
Languages : en
Pages : 232
Book Description
The Pontryagin Duality of Compact O-dimensional Semilattices and Its Applications
Author:
Publisher:
ISBN: 9780387068060
Category : Algebraic number theory
Languages : en
Pages : 201
Book Description
Publisher:
ISBN: 9780387068060
Category : Algebraic number theory
Languages : en
Pages : 201
Book Description
The Schur Subgroup of the Brauer Group
Author: Celia Witten
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
The Projective Schur Subgroup of the Brauer Group and Root Groups of Finite Groups
Author: P. Nelis
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
Brauer Groups in Ring Theory and Algebraic Geometry
Author: F. van Oystaeyen
Publisher: Springer
ISBN: 354039057X
Category : Mathematics
Languages : en
Pages : 312
Book Description
Publisher: Springer
ISBN: 354039057X
Category : Mathematics
Languages : en
Pages : 312
Book Description
Cohomology of Finite Groups
Author: Alejandro Adem
Publisher: Springer Science & Business Media
ISBN: 3662062801
Category : Mathematics
Languages : en
Pages : 329
Book Description
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N
Publisher: Springer Science & Business Media
ISBN: 3662062801
Category : Mathematics
Languages : en
Pages : 329
Book Description
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N
The Brauer–Grothendieck Group
Author: Jean-Louis Colliot-Thélène
Publisher: Springer Nature
ISBN: 3030742482
Category : Mathematics
Languages : en
Pages : 450
Book Description
This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
Publisher: Springer Nature
ISBN: 3030742482
Category : Mathematics
Languages : en
Pages : 450
Book Description
This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
Group Representations
Author:
Publisher: Elsevier
ISBN: 0080872913
Category : Mathematics
Languages : en
Pages : 925
Book Description
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups.The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.
Publisher: Elsevier
ISBN: 0080872913
Category : Mathematics
Languages : en
Pages : 925
Book Description
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups.The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.