##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## David Hansen

#### Columbia University

## Critical p-adic L-functions for Hilbert modular forms

##### Abstract:

I will describe a construction which associates a canonical $p$-adic L-function with a refined cohomological Hilbert modular form $(\pi, \alpha)$ under some mild and natural assumptions. The main novelty is that we do not impose any hypothesis of â€œsmall slopeâ€ or â€œnoncriticalityâ€ on the allowable refinements. Over $\mathbb{Q}$, this result is due to Bellaiche. Our strategy for dealing with critical refinements is roughly parallel to his, and in particular relies on a careful study of the local geometry of eigenvarieties at classical (but possibly critical) points. This is joint work with John Bergdall.

Host: Kiran Kedlaya

### December 2, 2016

### 1:00 PM

### AP&M 7321

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