##### Department of Mathematics,

University of California San Diego

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### Colloquium

## David Hansen

#### Columbia University

## Period maps in $p$-adic geometry

##### Abstract:

In classical Hodge theory, variations of Hodge structure and their associated period mappings play a crucial role. In the $p$-adic world, it turns out there are *two* natural kinds of period maps associated with variations of $p$-adic Hodge structure: the ``Grothendieck-Messing" period maps, which roughly come from comparing crystalline and de Rham cohomology, and the ``Hodge-Tate" period maps, which come from comparing de Rham and $p$-adic etale cohomology. I'll discuss these period maps, their applications, and some new results on their construction and geometry. This is partially joint work with Jared Weinstein.

Host: Kiran Kedlaya

### December 1, 2016

### 3:00 PM

### AP&M 6402

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