Special Year Seminar
p-adic Hodge Theory and Simpson’s Correspondence
This talk will introduce background, achievements and challenges in the quest to find non-Archimedean versions of the celebrated Corlette-Simpson correspondence, which on Kähler manifolds relates representations of the fundamental group to certain Higgs bundles.
In the non-Archimedean world, vector bundles for the v-topology on Scholze’s diamonds have proven to be a useful framework to study analogous problems. This leads to some results and many questions even beyond the scope of the classical setting. In particular, I will explain results for abeloid varieties obtained jointly with Ben Heuer, Lucas Mann and Mingjia Zhang.