Séminaire Arithmétique et Géométrie Algébrique
Moduli spaces in p-adic non-abelian Hodge theory
13
Dec. 2022
logo_team
Intervenant : Ben Heuer
Institution : Frankfurt University
Heure : 14h00 - 15h00
Lieu : Salle 3L15

In analogy to Simpson's complex non-abelian Hodge correspondence, the conjectural p-adic Simpson correspondence aims to relate p-adic representations of the étale fundamental group of a smooth proper rigid space X over C_p to Higgs bundles on X. I will discuss how this correspondence can be naturally rephrased as studying vector bundles on the pro-étale site of X. Based on this reformulation, I will explain how one can define p-adic analytic moduli spaces of representations and Higgs bundles, and how these give rise to a new geometric perspective on the p-adic Simpson correspondence in the case of curves. Surprisingly, in some respect, this seems to be better behaved than what one encounters in the complex theory.
 

All (past and future) events