## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Local \(\varepsilon\)-isomorphisms in families

**Speaker:** Rebecca Bellovin

**Speaker Info:** University of California, Berkeley

**Brief Description:**

**Special Note**:

**Abstract:**

Given a representation of \(\mathrm{Gal}_{\mathbf{Q}_p}\) with coefficients in a \(p\)-adically complete local ring \(R\), Fukaya and Kato have conjectured the existence of a canonical trivialization of the determinant of a certain cohomology complex. When \(R = \mathbf{Z}_p\) and the representation is a lattice in a de Rham representation, this trivialization should be related to the \(\varepsilon\)-factor of the corresponding Weil-Deligne
representation. Such a trivialization has been constructed for certain crystalline Galois representations, by the work of a number of authors. I will explain how to extend these trivializations to certain families of crystalline Galois representations. This is joint work with Otmar Venjakob.

**Date:** Monday, May 11, 2015

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Patrick Allen

**Contact email:** pballen@math.northwestern.edu

**Contact Phone:**

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