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Nearly ordinary rank four Galois representations and p-adic Siegel modular forms

Tilouine, J. (2006) Nearly ordinary rank four Galois representations and p-adic Siegel modular forms. Compositio Mathematica, 142 (5). pp. 1122-1156. ISSN 0010-437X. doi:10.1112/S0010437X06002119.

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This paper is devoted to the proof of two results. The first was conjectured in 1994 by the author. It concerns the identity, under certain assumptions, of the universal deformation ring of p-nearly ordinary Galois representations and a local component of the universal nearly ordinary Hecke algebra in the sense of Hida. The other, which relies on the first, concerns the modularity of certain abelian surfaces. More precisely, one can associate to certain irreducible abelian surfaces defined over the rationals overconvergent p-adic cusp eigenforms. The question of whether these forms are classical is not studied in this paper.

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Additional Information:© 2006 Foundation Compositio Mathematica. Published online: 25 September 2006. Received 10 February 2005, accepted in final form 11 January 2006. Part of this paper was written during visits at Nagoya University and at CalTech. The excellent working conditions in these institutions were appreciated. The author wishes to express his thanks to K. Fujiwara and D. Ramakrishnan for their invitation. Discussions with H. Hida, A. Mokrane and D. Blasius were also very useful. Finally, the author is also indebted to the referee whose careful reading helped to clarify several points.
Subject Keywords:Galois representations; Hecke algebras; Siegel varieties; congruences; p-adic modular forms
Issue or Number:5
Classification Code:MSC: 11F33; 11F46; 11F80 (primary); 11G18; 11F70 (secondary).
Record Number:CaltechAUTHORS:20110804-133301306
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Official Citation:Nearly ordinary rank four Galois representations and p-adic Siegel modular forms preview J. Tilouine Compositio Mathematica / Volume 142 / Issue 05, pp 1122 - 1156 Foundation Compositio Mathematica 2006 Published online: 25 September 2006 DOI:10.1112/S0010437X06002119
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24688
Deposited By: Ruth Sustaita
Deposited On:04 Aug 2011 21:51
Last Modified:09 Nov 2021 16:25

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