P-adic families of automorphic forms

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• David Loeffler (Imperial)
• Tuesday 19 February 2008, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Tim Dokchitser.

In this talk, I will discuss some of the remarkable p-adic continuity properties of automorphic forms. For classical modular forms, it was noted early on that there appear to exist p-adic families of Hecke eigenforms—q-expansions with coefficients that are formal power series in a variable k, which if evaluated at (some) positive integers k converge p-adically to the q-expansion of a Hecke eigenform.

In the 1990s Coleman and Mazur showed that all modular forms of finite slope may be interpolated in this way, and constructed a p-adic rigid space, the eigencurve, which can be regarded as a parameter space for such families. I shall give an introduction to the Coleman-Mazur theory, and describe some current research on analogous results for automorphic forms on higher-rank groups.

This talk is part of the Number Theory Seminar series.

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