Partial classicality of Hilbert modular forms

Abstract: Let $p$ be an inert prime in a totally real field $F$ for simplicity. Using the method of analytic continuation, Kassaei proved a classicality theorem: an overconvergent Hilbert $U_p$-eigenform is automatically classical when the slope is small compared to the weights. In analogy to overconvergent forms, which are defined over a strict neighborhood of the zero locus of the Hasse invariant, one can define partially classical overconvergent forms as defined over a strict neighborhood of the zero locus of a sub-collection of partial Hasse invariants. Under a weaker small slope condition depending on the relevant weights, we show that an overconvergent $U_p$-eigenform is partially classical.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.