Eigenvarieties for reductive groups

Pages 1685-1784 from Volume 174 (2011), Issue 3 by Eric Urban

Abstract

We develop the theory of overconvergent cohomology introduced by G. Stevens, and we use it to give a construction of eigenvarieties associated to any reductive group $G$ over $\mathbb{Q}$ such that $G(\mathbb{R})$ has discrete series. We prove that the so-called eigenvarieties are equidimensional and generically flat over the weight space.

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Keywords
, ,
DOI
http://doi.org/10.4007/annals.2011.174.3.7
MR
2846490
Zbl
06005483
Milestones
Received: 15 November 2008
Revised: 16 April 2010
Accepted: 30 September 2010
Published online: 1 November 2011

Authors

Eric Urban

Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027

Institut de Mathématique de Jussieu
Case 247 - 4
place Jussieu Cedex
75252 Paris Cedex
France