Simple Algebras and Relative Galois Cohomology PDF Download
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Author: Samuel Richard Mateosian
Publisher:
ISBN:
Category :
Languages : en
Pages : 96
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Book Description
Author: Samuel Richard Mateosian
Publisher:
ISBN:
Category :
Languages : en
Pages : 96
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Book Description
Author: Philippe Gille
Publisher: Cambridge University Press
ISBN: 1107156378
Category : Mathematics
Languages : en
Pages : 431
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Book Description
The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.
Author: Philippe Gille
Publisher: Cambridge University Press
ISBN: 1108293670
Category : Mathematics
Languages : en
Pages : 432
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Book Description
The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi–Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev–Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch–Gabber–Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics.
Author: Grégory Berhuy
Publisher: Cambridge University Press
ISBN: 1139490885
Category : Mathematics
Languages : en
Pages : 328
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Book Description
This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
Author: Donald Ross Ostberg
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 164
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Book Description
Author: Martin Kneser
Publisher:
ISBN:
Category : Algebra, Homological
Languages : en
Pages : 350
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Book Description
Author: Gille
Publisher:
ISBN: 9780521168915
Category :
Languages : en
Pages :
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Author: Jean-Louis Colliot-Thélène
Publisher: Springer Nature
ISBN: 3030742482
Category : Mathematics
Languages : en
Pages : 450
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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.
Author: Jean-Pierre Serre
Publisher: Springer Science & Business Media
ISBN: 3642591418
Category : Mathematics
Languages : en
Pages : 215
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Book Description
This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.
Author: Stephen Urban Chase
Publisher: American Mathematical Soc.
ISBN: 0821812521
Category : Commutative rings
Languages : en
Pages : 87
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Book Description
