On Families of Filtered phi Modules and Crystalline Representations

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:On Families of Filtered phi Modules and Crystalline Representations
Speaker:Eugen Hellmann
Affiliation:University of Bonn
Date:Wednesday, December 8
Time/Room:2:15pm - 3:15pm/S-101
Video Link:https://video.ias.edu/galois/hellman

We study families of filtered phi-modules associated to families of p-adic Galois representations as considered by Berger and Colmez. We show that the weakly admissible locus in a family of filtered phi-modules is open and that the groupoid of weakly admissible modules is in fact an Artin stack. Working in the category of adic spaces instead of the category of rigid analytic spaces one can show that there is an open substack of the weakly admissible locus over which the filtered phi-modules is induced from a family of crystalline representations.