Séminaire Arithmétique et Géométrie Algébrique
Moduli spaces in p-adic non-abelian Hodge theory
Dec. 2022
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.

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