Siqing Zhang, November 11, 2022

Title: Cohomological Non-Abelian Hodge Theorems in characteristic p

Abstract: We introduce two cohomological incarnations of the Non-Abelian Hodge Theorem for curves in characteristic p. Using the first one, we show that, in arbitrary characteristics, the cohomology ring of the moduli space of Higgs bundles is independent of the degree, as long as it is coprime to the rank. A closer analysis of the results above shows that, over the complex numbers, the Galois conjugation isomorphism between the character varieties preserves the perverse Leray filtrations induced by the Hitchin morphisms. Based on joint works with Mark de Cataldo, Michael Groechenig, Davesh Maulik, and Junliang Shen.