Etale Cohomology:
One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more gene...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, New Jersey
Princeton University Press
[1980]
|
| Schriftenreihe: | Princeton mathematical series
Band 33 |
| Schlagworte: | |
| Online-Zugang: | UBM01 Volltext |
| Zusammenfassung: | One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series |
| Beschreibung: | E-Book erschien 2016 |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781400883981 |
| DOI: | 10.1515/9781400883981 |
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| 520 | |a One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series | ||
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Sheaf theory | |
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Datensatz im Suchindex
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| author | Milne, J. S. 1942- |
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| author_sort | Milne, J. S. 1942- |
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| 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 | 10.1515/9781400883981 |
| format | Electronic eBook |
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| isbn | 9781400883981 |
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| spelling | Milne, J. S. 1942- Verfasser (DE-588)1077746881 aut Etale Cohomology James S. Milne Princeton, New Jersey Princeton University Press [1980] © 1980 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series Band 33 E-Book erschien 2016 One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series Geometry, Algebraic Homology theory Sheaf theory Etalkohomologie (DE-588)4153071-8 gnd rswk-swf Etalkohomologie (DE-588)4153071-8 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-08238-3 Princeton mathematical series Band 33 (DE-604)BV045898993 33 https://doi.org/10.1515/9781400883981 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Milne, J. S. 1942- Etale Cohomology Princeton mathematical series Geometry, Algebraic Homology theory Sheaf theory Etalkohomologie (DE-588)4153071-8 gnd |
| subject_GND | (DE-588)4153071-8 |
| title | Etale Cohomology |
| title_auth | Etale Cohomology |
| title_exact_search | Etale Cohomology |
| title_full | Etale Cohomology James S. Milne |
| title_fullStr | Etale Cohomology James S. Milne |
| title_full_unstemmed | Etale Cohomology James S. Milne |
| title_short | Etale Cohomology |
| title_sort | etale cohomology |
| topic | Geometry, Algebraic Homology theory Sheaf theory Etalkohomologie (DE-588)4153071-8 gnd |
| topic_facet | Geometry, Algebraic Homology theory Sheaf theory Etalkohomologie |
| url | https://doi.org/10.1515/9781400883981 |
| volume_link | (DE-604)BV045898993 |
| work_keys_str_mv | AT milnejs etalecohomology |