Rigid cohomology:
Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the se...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Cambridge tracts in mathematics
172 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas |
| Beschreibung: | 1 Online-Ressource (xv, 319 Seiten) |
| ISBN: | 9780511543128 |
| DOI: | 10.1017/CBO9780511543128 |
Internformat
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| 505 | 8 | 0 | |g 1.1 |g 1 |t Alice and Bob |g 1.2 |g 2 |t Complexity |g 1.3 |g 3 |t Weil conjectures |g 1.4 |g 4 |t Zeta functions |g 1.5 |g 5 |t Arithmetic cohomology |g 1.6 |g 6 |t Bloch-Ogus cohomology |g 1.7 |g 7 |t Frobenius on rigid cohomology |g 1.8 |g 8 |t Slopes of Frobenius |g 1.9 |g 9 |t The coefficients question |g 1.10 |g 9 |t F-isocrystals |g 2 |g 12 |t Tubes |g 2.1 |g 12 |t Some rigid geometry |g 2.2 |g 16 |t Tubes of radius one |g 2.3 |g 23 |t Tubes of smaller radius |g 3 |g 35 |t Strict neighborhoods |g 3.1 |g 35 |t Frames |g 3.2 |g 43 |t Frames and tubes |g 3.3 |g 54 |t Strict neighborhoods and tubes |g 3.4 |g 65 |t Standard neighborhoods |g 4 |g 74 |t Calculus |g 4.1 |g 74 |t Calculus in rigid analytic geometry |g 4.3 |g 97 |t Calculus on strict neighborhoods |g 4.4 |g 107 |t Radius of convergence |g 5 |g 125 |t Overconvergent sheaves |g 5.1 |g 125 |t Overconvergent sections |g 5.2 |g 137 |t Overconvergence and abelian sheaves |g 5.3 |g 153 |t Dagger modules |g 5.4 |g 160 |t Coherent dagger modules |g 6 |g 177 |t Overconvergent calculus |g 6.1 |g 177 |t Stratifications and overconvergence |g 6.2 |g 184 |t Cohomology |g 6.3 |g 192 |t Cohomology with support in a closed subset |g 6.4 |t Cohomology with compact support |
| 520 | |a Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas | ||
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Datensatz im Suchindex
| _version_ | 1804176883691028480 |
|---|---|
| any_adam_object | |
| author | Le Stum, Bernard 1959- |
| author_GND | (DE-588)1023217325 |
| author_facet | Le Stum, Bernard 1959- |
| author_role | aut |
| author_sort | Le Stum, Bernard 1959- |
| author_variant | s b l sb sbl |
| building | Verbundindex |
| bvnumber | BV043941650 |
| classification_rvk | SK 320 |
| collection | ZDB-20-CBO |
| contents | Alice and Bob Complexity Weil conjectures Zeta functions Arithmetic cohomology Bloch-Ogus cohomology Frobenius on rigid cohomology Slopes of Frobenius The coefficients question F-isocrystals Tubes Some rigid geometry Tubes of radius one Tubes of smaller radius Strict neighborhoods Frames Frames and tubes Strict neighborhoods and tubes Standard neighborhoods Calculus Calculus in rigid analytic geometry Calculus on strict neighborhoods Radius of convergence Overconvergent sheaves Overconvergent sections Overconvergence and abelian sheaves Dagger modules Coherent dagger modules Overconvergent calculus Stratifications and overconvergence Cohomology Cohomology with support in a closed subset Cohomology with compact support |
| ctrlnum | (ZDB-20-CBO)CR9780511543128 (OCoLC)850421760 (DE-599)BVBBV043941650 |
| dewey-full | 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.23 |
| dewey-search | 514.23 |
| dewey-sort | 3514.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543128 |
| format | Electronic eBook |
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| id | DE-604.BV043941650 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511543128 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350620 |
| oclc_num | 850421760 |
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| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xv, 319 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Le Stum, Bernard 1959- Verfasser (DE-588)1023217325 aut Rigid cohomology Bernard Le Stum Cambridge Cambridge University Press 2007 1 Online-Ressource (xv, 319 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 172 1.1 1 Alice and Bob 1.2 2 Complexity 1.3 3 Weil conjectures 1.4 4 Zeta functions 1.5 5 Arithmetic cohomology 1.6 6 Bloch-Ogus cohomology 1.7 7 Frobenius on rigid cohomology 1.8 8 Slopes of Frobenius 1.9 9 The coefficients question 1.10 9 F-isocrystals 2 12 Tubes 2.1 12 Some rigid geometry 2.2 16 Tubes of radius one 2.3 23 Tubes of smaller radius 3 35 Strict neighborhoods 3.1 35 Frames 3.2 43 Frames and tubes 3.3 54 Strict neighborhoods and tubes 3.4 65 Standard neighborhoods 4 74 Calculus 4.1 74 Calculus in rigid analytic geometry 4.3 97 Calculus on strict neighborhoods 4.4 107 Radius of convergence 5 125 Overconvergent sheaves 5.1 125 Overconvergent sections 5.2 137 Overconvergence and abelian sheaves 5.3 153 Dagger modules 5.4 160 Coherent dagger modules 6 177 Overconvergent calculus 6.1 177 Stratifications and overconvergence 6.2 184 Cohomology 6.3 192 Cohomology with support in a closed subset 6.4 Cohomology with compact support Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd rswk-swf Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Kristalline Kohomologie (DE-588)4494390-8 s Verallgemeinerung (DE-588)4316262-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-87524-0 https://doi.org/10.1017/CBO9780511543128 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Le Stum, Bernard 1959- Rigid cohomology Alice and Bob Complexity Weil conjectures Zeta functions Arithmetic cohomology Bloch-Ogus cohomology Frobenius on rigid cohomology Slopes of Frobenius The coefficients question F-isocrystals Tubes Some rigid geometry Tubes of radius one Tubes of smaller radius Strict neighborhoods Frames Frames and tubes Strict neighborhoods and tubes Standard neighborhoods Calculus Calculus in rigid analytic geometry Calculus on strict neighborhoods Radius of convergence Overconvergent sheaves Overconvergent sections Overconvergence and abelian sheaves Dagger modules Coherent dagger modules Overconvergent calculus Stratifications and overconvergence Cohomology Cohomology with support in a closed subset Cohomology with compact support Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| subject_GND | (DE-588)4494390-8 (DE-588)4316262-9 |
| title | Rigid cohomology |
| title_alt | Alice and Bob Complexity Weil conjectures Zeta functions Arithmetic cohomology Bloch-Ogus cohomology Frobenius on rigid cohomology Slopes of Frobenius The coefficients question F-isocrystals Tubes Some rigid geometry Tubes of radius one Tubes of smaller radius Strict neighborhoods Frames Frames and tubes Strict neighborhoods and tubes Standard neighborhoods Calculus Calculus in rigid analytic geometry Calculus on strict neighborhoods Radius of convergence Overconvergent sheaves Overconvergent sections Overconvergence and abelian sheaves Dagger modules Coherent dagger modules Overconvergent calculus Stratifications and overconvergence Cohomology Cohomology with support in a closed subset Cohomology with compact support |
| title_auth | Rigid cohomology |
| title_exact_search | Rigid cohomology |
| title_full | Rigid cohomology Bernard Le Stum |
| title_fullStr | Rigid cohomology Bernard Le Stum |
| title_full_unstemmed | Rigid cohomology Bernard Le Stum |
| title_short | Rigid cohomology |
| title_sort | rigid cohomology |
| topic | Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| topic_facet | Homology theory Kristalline Kohomologie Verallgemeinerung |
| url | https://doi.org/10.1017/CBO9780511543128 |
| work_keys_str_mv | AT lestumbernard rigidcohomology |