Diamantine Picard varieties and the p-adic Simpson correspondence in rank one
Dr. Ben Heuer
2023-05-09 10:00-11:00
MCM210
Speaker: Dr. Ben Heuer (Institut für Mathematik, Johann Wolfgang Goethe-Universität)Time: 10:00-11:00 May 9, 2023 (Tuesday)
Place: MCM210
Title: Diamantine Picard varieties and the p-adic Simpson correspondence in rank one
Abstract: In p-adic geometry, the rigid analytic Picard variety of a proper rigid space X is a moduli space of line bundles. In this talk, I will discuss new versions of the Picard functor defined instead of perfectoid test objects. One interesting aspect visible from this "diamantine" perspective is the difference between line bundles in different p-adic topologies. I will discuss two applications: First, I will explain what we can learn from this about the structure of rigid Picard varieties. Second, we use the diamantine Picard functor to construct the p-adic Simpson correspondence for continuous characters of the fundamental group of X. This also gives new insights into what the correct formulation of the p-adic Simpson correspondence should be in general.
