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The Brauer Grothendieck Group (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 71) free ebook download

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Author(s):	Jean-Louis Colliot-Thelene

Date:	2021	Format:	7z	Language:	English	ISBN/ASIN:	3030742474
Pages:	468	OCR:		Quality:		ISBN13:
Uploader:	topron	Upload Date:	8/4/2021 11:44:25 AM

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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 BrauerManin 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 Jongs proof of Gabbers theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the BrauerManin 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 BrauerGrothendieck 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.

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The Brauer Grothendieck Group (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 71) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics