The Brauer-Grothendieck Group (Record no. 60503)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03166 a2200265 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240808b2021 |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783030742478 (HB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 51 |
| Item number | THE |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Thelene, Jean-Louis Colliot |
| 245 ## - TITLE STATEMENT | |
| Title | The Brauer-Grothendieck Group |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher | Springer |
| Year of publication | 2021 |
| Place of publication | Switzerland |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xv, 453p. |
| 490 ## - SERIES STATEMENT | |
| Series statement | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 |
| Volume number/sequential designation | 71 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes Bibliography (427-448) and Index |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Galois Cohomology<br/>2. Étale Cohomology<br/>3. Brauer Groups of Schemes<br/>4. Comparison of the Two Brauer Groups, II<br/>5. Varieties Over a Field<br/>6. Birational Invariance<br/>7. Severi-Brauer Varieties and hypersurfaces<br/>8. Singular Schemes and Varieties<br/>9. Varieties with a Group Action<br/>10. Schemes Over Local Rings and Fields<br/>11. Families of Varieties<br/>12. Rationality in a Family<br/>13. The Brauer-Manin Set and the formal lemma<br/>14. Rational Points in the Brauer-Manin Set<br/>15. The Brauer-Manin Obstruction for Zero-Cycles<br/>16. The Tate Conjecture, Abelian Varieties and K3 Surfaces |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Arithmetical algebraic geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Brauer group |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Cohomology operations |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Grothendieck groups |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Skorobogatov, Alexei N. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Shelving location | Full call number | Accession Number | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | First Floor, Rack No: 27, Shelf No: 36 | 51 THE | 78181 | BOOKS |