On classicality of overconvergent $p$-adic automorphic forms

Abstract: I will report on some positive and a negative result concerning the question whether a given overconvergent $p$-adic eigenform of finite slope is classical or not. The positive result is the generalization of a classicality statement (obtained in earlier joint work with Breuil and Schraen) to the case of semi-stable Galois representations. This classicality result is rather a statement about the Galois representation attached to a $p$-adic automorphic form than a statement about the $p$-adic automorphic form itself. The negative result concerns the classicality problem for the $p$-adic automorphic form itself. If time permits we will discuss some conjectural picture explaining this negative result.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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