## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Integral structures on de Rham cohomology

**Speaker:** Andrew Snowden

**Speaker Info:** MIT

**Brief Description:**

**Special Note**: **There will be an introductory preseminar talk 2:00-2:45 in 101 Annenberg.**

**Abstract:**

Associated to a smooth projective variety over the rational numbers are its
algebraic de Rham cohomology groups, which are finite dimensional rational
vector spaces. I will show how one can construct certain natural
lattices in these vector spaces. The construction of these integral structures
is analogous to Deligne's construction of the "canonical extension" in the
theory of variation of Hodge structures, with p-adic Hodge theory taking the
place of usual Hodge theory. I will briefly review the complex theory,
explain the construction in the arithmetic setting and then give some examples
and applications. This is joint work with Bhargav Bhatt.

**Date:** Monday, November 21, 2011

**Time:** 3:00PM

**Where:** 107 Lunt

**Contact Person:** Ellen Eischen

**Contact email:** eeischen@math

**Contact Phone:** 847-467-1891

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