|
|
|
|
| LEADER |
00000cam a2200000 i 4500 |
| 001 |
on1262553647 |
| 003 |
OCoLC |
| 005 |
20240909213021.0 |
| 006 |
m o d |
| 007 |
cr cnu---unuuu |
| 008 |
210802s2021 sz ob 001 0 eng d |
| 040 |
|
|
|a YDX
|b eng
|e rda
|e pn
|c YDX
|d GW5XE
|d EBLCP
|d YDX
|d OCLCO
|d OCLCF
|d OCLCQ
|d OCLCO
|d OCLCQ
|d SFB
|d OCLCO
|d S9M
|d OCLCL
|d S9M
|
| 019 |
|
|
|a 1263029018
|
| 020 |
|
|
|a 9783030742485
|q (electronic bk.)
|
| 020 |
|
|
|a 3030742482
|q (electronic bk.)
|
| 020 |
|
|
|z 3030742474
|
| 020 |
|
|
|z 9783030742478
|
| 024 |
7 |
|
|a 10.1007/978-3-030-74248-5
|2 doi
|
| 035 |
|
|
|a (OCoLC)1262553647
|z (OCoLC)1263029018
|
| 050 |
|
4 |
|a QA174.2
|b .C65 2021
|
| 072 |
|
7 |
|a PBMW
|2 bicssc
|
| 072 |
|
7 |
|a MAT012010
|2 bisacsh
|
| 072 |
|
7 |
|a PBMW
|2 thema
|
| 049 |
|
|
|a HCDD
|
| 100 |
1 |
|
|a Colliot-Thélène, J.-L.
|q (Jean-Louis),
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PBJvd6MYfMyRVk3cWQVmjmd
|
| 245 |
1 |
4 |
|a The Brauer-Grothendieck group /
|c Jean-Louis Colliot-Thélène, Alexei N. Skorobogatov.
|
| 264 |
|
1 |
|a Cham, Switzerland :
|b Springer,
|c 2021.
|
| 300 |
|
|
|a 1 online resource
|
| 336 |
|
|
|a text
|b txt
|2 rdacontent
|
| 337 |
|
|
|a computer
|b c
|2 rdamedia
|
| 338 |
|
|
|a online resource
|b cr
|2 rdacarrier
|
| 490 |
1 |
|
|a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,
|x 0071-1136 ;
|v v. 71
|
| 505 |
0 |
|
|a 1 Galois Cohomology -- 2 Étale Cohomology -- 3 Brauer Groups of Schemes -- 4 Comparison of the Two Brauer Groups, II -- 5 Varieties Over a Field -- 6 Birational Invariance -- 7 Severi rauer Varieties and Hypersurfaces -- 8 Singular Schemes and Varieties -- 9 Varieties with a Group Action -- 10 Schemes Over Local Rings and Fields -- 11 Families of Varieties -- 12 Rationality in a Family -- 13 The Brauer anin Set and the Formal Lemma -- 14 Are Rational Points Dense in the Brauer anin Set? -- 15 The Brauer anin Obstruction for Zero-Cycles -- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces -- Bibliography -- Index.
|
| 504 |
|
|
|a Includes bibliographical references and index.
|
| 520 |
|
|
|a 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 anin 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 proof of Gabber theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer anin 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.
|
| 588 |
0 |
|
|a Online resource; title from PDF title page (SpringerLink, viewed August 10, 2021).
|
| 650 |
|
0 |
|a Grothendieck groups.
|
| 650 |
|
0 |
|a Brauer groups.
|
| 650 |
|
7 |
|a Teoría de grupos
|2 embne
|
| 650 |
0 |
7 |
|a Group theory
|2 embucm
|
| 650 |
|
7 |
|a Brauer groups
|2 fast
|
| 650 |
|
7 |
|a Grothendieck groups
|2 fast
|
| 650 |
|
7 |
|a Grups de Brauer.
|2 thub
|
| 655 |
|
7 |
|a Llibres electrònics.
|2 thub
|
| 700 |
1 |
|
|a Skorobogatov, Alexei,
|d 1961-
|e author
|1 https://id.oclc.org/worldcat/entity/E39PBJh8JRMc9pF8B7cHd6Dcyd
|1 https://orcid.org/0000-0002-9309-2615
|
| 758 |
|
|
|i has work:
|a The Brauer-Grothendieck group (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCFPWR9yTv6DXvkpDfxkQ7b
|4 https://id.oclc.org/worldcat/ontology/hasWork
|
| 776 |
0 |
8 |
|c Original
|z 3030742474
|z 9783030742478
|w (OCoLC)1242465146
|
| 830 |
|
0 |
|a Ergebnisse der Mathematik und ihrer Grenzgebiete ;
|v 3. Folge, Bd. 71.
|x 0071-1136
|
| 856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-030-74248-5
|y Click for online access
|
| 903 |
|
|
|a SPRING-MATH2021
|
| 994 |
|
|
|a 92
|b HCD
|