EVENT DETAILS AND ABSTRACT

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.