Euler Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2000]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 147 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry |
| Beschreibung: | 1 Online-Ressource (240p.) |
| ISBN: | 9781400865208 |
| DOI: | 10.1515/9781400865208 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 147 | |
| 500 | |a One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry | ||
| 546 | |a In English | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Algebraic number theory | |
| 650 | 4 | |a p-adic numbers | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Rubin, Karl |
| author_facet | Rubin, Karl |
| author_role | aut |
| author_sort | Rubin, Karl |
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| building | Verbundindex |
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| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.74 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400865208 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:24:04Z |
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| isbn | 9781400865208 |
| language | English |
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| spelling | Rubin, Karl Verfasser aut Euler Systems Karl Rubin Princeton, N.J. Princeton University Press [2000] © 2000 1 Online-Ressource (240p.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 147 One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry In English Mathematik Algebraic number theory p-adic numbers MATHEMATICS / Algebra / Intermediate MATHEMATICS / Number Theory bisacsh p-adische L-Funktion (DE-588)4398270-0 gnd rswk-swf Galois-Kohomologie (DE-588)4019172-2 gnd rswk-swf Kreiskörper (DE-588)4165607-6 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf p-adische L-Funktion (DE-588)4398270-0 s Galois-Kohomologie (DE-588)4019172-2 s Kreiskörper (DE-588)4165607-6 s Elliptische Kurve (DE-588)4014487-2 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-05075-9 Annals of Mathematics Studies number 147 (DE-604)BV040389493 147 https://doi.org/10.1515/9781400865208?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rubin, Karl Euler Systems Annals of Mathematics Studies Mathematik Algebraic number theory p-adic numbers MATHEMATICS / Algebra / Intermediate MATHEMATICS / Number Theory bisacsh p-adische L-Funktion (DE-588)4398270-0 gnd Galois-Kohomologie (DE-588)4019172-2 gnd Kreiskörper (DE-588)4165607-6 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4398270-0 (DE-588)4019172-2 (DE-588)4165607-6 (DE-588)4014487-2 |
| title | Euler Systems |
| title_auth | Euler Systems |
| title_exact_search | Euler Systems |
| title_full | Euler Systems Karl Rubin |
| title_fullStr | Euler Systems Karl Rubin |
| title_full_unstemmed | Euler Systems Karl Rubin |
| title_short | Euler Systems |
| title_sort | euler systems |
| topic | Mathematik Algebraic number theory p-adic numbers MATHEMATICS / Algebra / Intermediate MATHEMATICS / Number Theory bisacsh p-adische L-Funktion (DE-588)4398270-0 gnd Galois-Kohomologie (DE-588)4019172-2 gnd Kreiskörper (DE-588)4165607-6 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Mathematik Algebraic number theory p-adic numbers MATHEMATICS / Algebra / Intermediate MATHEMATICS / Number Theory p-adische L-Funktion Galois-Kohomologie Kreiskörper Elliptische Kurve |
| url | https://doi.org/10.1515/9781400865208?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT rubinkarl eulersystems |