Eigenvarieties for reductive groups

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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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