Local geometry of moduli stacks of two-dimensional Galois representations

Abstract

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, as well as their resolutions by moduli stacks of two-dimensional Breuil-Kisin modules with tame descent data. We study the local geometry of these moduli stacks by comparing them with local models of Shimura varieties at hyperspecial and Iwahori level.

arXiv commentTo appear, Proceedings of the International Colloquium on 'Arithmetic Geometry', TIFR Mumbai, Jan. 6-10, 2020. Comprises portions of the unpublished arXiv:1908.07019. 55 pages