Arithmetic Compactifications of PEL-Type Shimura Varieties
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Princeton, N.J.
Princeton University Press
[2013]
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| Schriftenreihe: | London Mathematical Society Monographs
36 |
| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-Aug4 DE-859 DE-860 DE-739 Volltext |
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| 500 | |a By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai) | ||
| 546 | |a In English | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Shimura varieties | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a MATHEMATICS / Geometry / Algebraic | |
| 650 | 4 | |a MATHEMATICS / Geometry / General | |
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Datensatz im Suchindex
| _version_ | 1819294458745716736 |
|---|---|
| any_adam_object | |
| author | Lan, Kai-Wen |
| author_facet | Lan, Kai-Wen |
| author_role | aut |
| author_sort | Lan, Kai-Wen |
| author_variant | k w l kwl |
| building | Verbundindex |
| bvnumber | BV042523087 |
| collection | ZDB-23-DGG |
| ctrlnum | (OCoLC)832314069 (DE-599)BVBBV042523087 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400846016 |
| format | Electronic eBook |
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| id | DE-604.BV042523087 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:26:35Z |
| institution | BVB |
| isbn | 9781400846016 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027957426 |
| oclc_num | 832314069 |
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| physical | 1 Online-Ressource (584p.) |
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| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | Princeton University Press |
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| series2 | London Mathematical Society Monographs |
| spelling | Lan, Kai-Wen Verfasser aut Arithmetic Compactifications of PEL-Type Shimura Varieties Kai-Wen Lan Princeton, N.J. Princeton University Press [2013] 1 Online-Ressource (584p.) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society Monographs 36 By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai) In English Mathematik Shimura varieties Arithmetical algebraic geometry MATHEMATICS / Geometry / Algebraic MATHEMATICS / Geometry / General https://doi.org/10.1515/9781400846016 Verlag Volltext |
| spellingShingle | Lan, Kai-Wen Arithmetic Compactifications of PEL-Type Shimura Varieties Mathematik Shimura varieties Arithmetical algebraic geometry MATHEMATICS / Geometry / Algebraic MATHEMATICS / Geometry / General |
| title | Arithmetic Compactifications of PEL-Type Shimura Varieties |
| title_auth | Arithmetic Compactifications of PEL-Type Shimura Varieties |
| title_exact_search | Arithmetic Compactifications of PEL-Type Shimura Varieties |
| title_full | Arithmetic Compactifications of PEL-Type Shimura Varieties Kai-Wen Lan |
| title_fullStr | Arithmetic Compactifications of PEL-Type Shimura Varieties Kai-Wen Lan |
| title_full_unstemmed | Arithmetic Compactifications of PEL-Type Shimura Varieties Kai-Wen Lan |
| title_short | Arithmetic Compactifications of PEL-Type Shimura Varieties |
| title_sort | arithmetic compactifications of pel type shimura varieties |
| topic | Mathematik Shimura varieties Arithmetical algebraic geometry MATHEMATICS / Geometry / Algebraic MATHEMATICS / Geometry / General |
| topic_facet | Mathematik Shimura varieties Arithmetical algebraic geometry MATHEMATICS / Geometry / Algebraic MATHEMATICS / Geometry / General |
| url | https://doi.org/10.1515/9781400846016 |
| work_keys_str_mv | AT lankaiwen arithmeticcompactificationsofpeltypeshimuravarieties |