##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Daxin Xu

#### Caltech

## Parallel transport and the $p$-adic Simpson correspondence

##### Abstract:

Deninger and Werner developed an analogue for $p$-adic curves of the classical correspondence of Narasimhan and Seshadri between stable bundles of degree zero and unitary representations of the topological fundamental group for a complex smooth proper curve. Using parallel transport, they associated functorially to every vector bundle on a $p$-adic curve whose reduction is strongly semi-stable of degree 0 a $p$-adic representation of the \'etale fundamental group of the curve. They asked several questions: whether their functor is fully faithful and what is its essential image; whether the cohomology of the local systems produced by this functor admits a Hodge-Tate filtration; and whether their construction is compatible with the $p$-adic Simpson correspondence developed by Faltings. We will answer these questions in this talk.

Host: Kiran Kedlaya

### January 25, 2018

### 1:00 PM

### AP&M 7321

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