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Eigenvarieties for reductive groups. (English) Zbl 1285.11081

Author’s abstract: We develop the theory of overconvergent cohomology introduced by G. Stevens [Overconvergent modular symbols and a conjecture of Mazur, Tate, and Teitelbaum. Preprint], 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.

MSC:

11F85 \(p\)-adic theory, local fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
11F75 Cohomology of arithmetic groups
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