Mumford-Tate groups and domains: their geometry and arithmetic
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2012]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 183 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Biographical note: Mark Green is professor of mathematics at the University of California, Los Angeles and is Director Emeritus of the Institute for Pure and Applied Mathematics. Phillip A. Griffiths is Professor Emeritus of Mathematics and former director at the Institute for Advanced Study in Princeton. Matt Kerr is assistant professor of mathematics at Washington University in St. Louis Main description: Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject |
| Beschreibung: | 1 Online-Ressource (288 S.) |
| ISBN: | 9781400842735 |
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| 500 | |a Main description: Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject | ||
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9781400842735 |
| language | English |
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| publishDate | 2012 |
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| spelling | Green, Mark 1947- (DE-588)129505234 aut Mumford-Tate groups and domains their geometry and arithmetic Princeton, N.J. Princeton University Press [2012] © 2012 1 Online-Ressource (288 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 183 Biographical note: Mark Green is professor of mathematics at the University of California, Los Angeles and is Director Emeritus of the Institute for Pure and Applied Mathematics. Phillip A. Griffiths is Professor Emeritus of Mathematics and former director at the Institute for Advanced Study in Princeton. Matt Kerr is assistant professor of mathematics at Washington University in St. Louis Main description: Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject Mumford-Tate-Gruppe (DE-588)4614885-1 gnd rswk-swf Mumford-Tate-Gruppe (DE-588)4614885-1 s 1\p DE-604 Griffiths, Phillip 1938- (DE-588)131881434 aut Kerr, Matt 1975- (DE-588)1022666991 aut Erscheint auch als Druck-Ausgabe 978-0-691-15424-4 Annals of Mathematics Studies number 183 (DE-604)BV040389493 183 http://www.degruyter.com/doi/book/10.1515/9781400842735?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400842735&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Green, Mark 1947- Griffiths, Phillip 1938- Kerr, Matt 1975- Mumford-Tate groups and domains their geometry and arithmetic Annals of Mathematics Studies Mumford-Tate-Gruppe (DE-588)4614885-1 gnd |
| subject_GND | (DE-588)4614885-1 |
| title | Mumford-Tate groups and domains their geometry and arithmetic |
| title_auth | Mumford-Tate groups and domains their geometry and arithmetic |
| title_exact_search | Mumford-Tate groups and domains their geometry and arithmetic |
| title_full | Mumford-Tate groups and domains their geometry and arithmetic |
| title_fullStr | Mumford-Tate groups and domains their geometry and arithmetic |
| title_full_unstemmed | Mumford-Tate groups and domains their geometry and arithmetic |
| title_short | Mumford-Tate groups and domains |
| title_sort | mumford tate groups and domains their geometry and arithmetic |
| title_sub | their geometry and arithmetic |
| topic | Mumford-Tate-Gruppe (DE-588)4614885-1 gnd |
| topic_facet | Mumford-Tate-Gruppe |
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