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001438630 001__ 1438630
001438630 003__ OCoLC
001438630 005__ 20230309004345.0
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001438630 019__ $$a1263029018
001438630 020__ $$a9783030742485$$q(electronic bk.)
001438630 020__ $$a3030742482$$q(electronic bk.)
001438630 020__ $$z3030742474
001438630 020__ $$z9783030742478
001438630 0247_ $$a10.1007/978-3-030-74248-5$$2doi
001438630 035__ $$aSP(OCoLC)1262553647
001438630 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dYDX$$dOCLCO$$dOCLCF$$dOCLCQ$$dOCLCO$$dOCLCQ
001438630 049__ $$aISEA
001438630 050_4 $$aQA174.2$$b.C65 2021
001438630 08204 $$a512/.46$$223
001438630 1001_ $$aColliot-Thélène, J.-L.$$q(Jean-Louis),$$eauthor.
001438630 24514 $$aThe Brauer-Grothendieck group /$$cJean-Louis Colliot-Thélène, Alexei N. Skorobogatov.
001438630 264_1 $$aCham, Switzerland :$$bSpringer,$$c2021.
001438630 300__ $$a1 online resource
001438630 336__ $$atext$$btxt$$2rdacontent
001438630 337__ $$acomputer$$bc$$2rdamedia
001438630 338__ $$aonline resource$$bcr$$2rdacarrier
001438630 4901_ $$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$$x0071-1136 ;$$vv. 71
001438630 504__ $$aIncludes bibliographical references and index.
001438630 5050_ $$a1 Galois Cohomology -- 2 Étale Cohomology -- 3 Brauer Groups of Schemes -- 4 Comparison of the Two Brauer Groups, II -- 5 Varieties Over a Field -- 6 Birational Invariance -- 7 Severi rauer Varieties and Hypersurfaces -- 8 Singular Schemes and Varieties -- 9 Varieties with a Group Action -- 10 Schemes Over Local Rings and Fields -- 11 Families of Varieties -- 12 Rationality in a Family -- 13 The Brauer anin Set and the Formal Lemma -- 14 Are Rational Points Dense in the Brauer anin Set? -- 15 The Brauer anin Obstruction for Zero-Cycles -- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces -- Bibliography -- Index.
001438630 506__ $$aAccess limited to authorized users.
001438630 520__ $$aThis monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer anin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong proof of Gabber theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer anin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer-Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
001438630 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed August 10, 2021).
001438630 650_0 $$aGrothendieck groups.
001438630 650_0 $$aBrauer groups.
001438630 650_6 $$aGroupes de Grothendieck.
001438630 650_6 $$aGroupes de Brauer.
001438630 655_0 $$aElectronic books.
001438630 7001_ $$aSkorobogatov, Alexei,$$d1961-$$eauthor$$1https://orcid.org/0000-0002-9309-2615
001438630 77608 $$iPrint version: $$z3030742474$$z9783030742478$$w(OCoLC)1242465146
001438630 830_0 $$aErgebnisse der Mathematik und ihrer Grenzgebiete ;$$v3. Folge, Bd. 71.$$x0071-1136
001438630 852__ $$bebk
001438630 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-74248-5$$zOnline Access$$91397441.1
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