Jorza, Andrei (2013) Galois representations for holomorphic Siegel modular forms. Mathematische Annalen, 355 (1). pp. 381-400. ISSN 0025-5831. doi:10.1007/s00208-012-0811-3. https://resolver.caltech.edu/CaltechAUTHORS:20130204-101236206
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Abstract
We prove local–global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert–Siegel modular forms in many cases (induced from Borel or Klingen parabolic), and as a corollary we obtain a conjecture of Skinner and Urban. For Siegel modular forms, when the local representation is an irreducible principal series we get local–global compatibility without a twist. We achieve this by proving a version of rigidity (strong multiplicity one) for GSp(4) using, on the one hand the doubling method to compute the standard L-function, and on the other hand the explicit classification of the irreducible local representations of GSp(4) over p-adic fields; then we use the existence of a globally generic Hilbert–Siegel modular form weakly equivalent to the original and we refer to Sorensen (Mathematica 15:623–670, 2010) for local–global compatibility in that case.
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| Additional Information: | © 2012 Springer-Verlag. Received: 7 July 2011; Revised: 14 February 2012; Published online: 13 April 2012. This work was motivated by the author’s thesis, written under the supervision of Andrew Wiles, and we are grateful to him and to Chris Skinner for suggesting the problem and for his invaluable help. We would like to thank Dinakar Ramakrishnan for his guidance in the final stages of this project, and Claus Sørensen for many helpful discussions. Most of this article was written while the author was a member of the Institute for Advanced Study, supported by the National Science Foundation grant DMS-0635607. We would like to thank the organizers of the special year on Galois Representations for a wonderful research experience. We would like to acknowledge helpful conversations with Wee Teck Gan, Erez Lapid and Shuichiro Takeda. | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | Mathematics Subject Classification: 11F80; 11F46; 11F70; 11R39 | |||||||||
| DOI: | 10.1007/s00208-012-0811-3 | |||||||||
| Record Number: | CaltechAUTHORS:20130204-101236206 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130204-101236206 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 36752 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 05 Feb 2013 23:21 | |||||||||
| Last Modified: | 09 Nov 2021 23:24 |
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