Cohomological Theory of Crystals over Function Fields (Record no. 50409)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03254nam a22004095a 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783037195741 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Böckle, Gebhard, |
| 245 10 - TITLE STATEMENT | |
| Title | Cohomological Theory of Crystals over Function Fields |
| Statement of responsibility, etc | Gebhard Böckle, Richard Pink |
| 260 3# - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Zuerich, Switzerland : |
| Name of publisher | European Mathematical Society Publishing House, |
| Year of publication | 2009 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (195 pages) |
| 490 0# - SERIES STATEMENT | |
| Series statement | EMS Tracts in Mathematics (ETM) |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book develops a new cohomological theory for schemes in positive characteristic p and it applies this theory to give a purely algebraic proof of a conjecture of Goss on the rationality of certain L-functions arising in the arithmetic of function fields. These L-functions are power series over a certain ring A, associated to any family of Drinfeld A-modules or, more generally, of A-motives on a variety of finite type over the finite field Fp. By analogy to the Weil conjecture, Goss conjectured that these L-functions are in fact rational functions. In 1996 Taguchi and Wan gave a first proof of Goss’s conjecture by analytic methods à la Dwork. The present text introduces A-crystals, which can be viewed as generalizations of families of A-motives, and studies their cohomology. While A-crystals are defined in terms of coherent sheaves together with a Frobenius map, in many ways they actually behave like constructible étale sheaves. A central result is a Lefschetz trace formula for L-functions of A-crystals, from which the rationality of these L-functions is immediate. Beyond its application to Goss’s L-functions, the theory of A-crystals is closely related to the work of Emerton and Kisin on unit root F-crystals, and it is essential in an Eichler–Shimura type isomorphism for Drinfeld modular forms as constructed by the first author. The book is intended for researchers and advanced graduate students interested in the arithmetic of function fields and/or cohomology theories for varieties in positive characteristic. It assumes a good working knowledge in algebraic geometry as well as familiarity with homological algebra and derived categories, as provided by standard textbooks. Beyond that the presentation is largely self-contained. |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Analytic number theory |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Number theory |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebraic geometry |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Böckle, Gebhard, |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Pink, Richard, |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.4171/074 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.ems-ph.org/img/books/boeckle_mini.jpg |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Zuerich, Switzerland : |
| -- | European Mathematical Society Publishing House, |
| -- | 2009 |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK13785 | https://doi.org/10.4171/074 | E-BOOKS |