On local Galois deformation rings

Abstract: We show that framed deformation rings of mod $p$ representations of the absolute Galois group of a $p$-adic local field are complete intersections of expected dimension. We determine their irreducible components and show that they and their special fibres are normal and complete intersection. As an application we prove density results of loci with prescribed $p$-adic Hodge theoretic properties.

(joint work with Gebhard Boeckle and Ashwin Iyengar. The preprint is available at arxiv.org/abs/2110.01638 ).

number theory

Audience: researchers in the topic

Columbia CUNY NYU number theory seminar