MIT Lie Groups Seminar

Building 2, 2-142

Speaker: Mingjia Zhang (Princeton University)Title: p-adic Simpson correspondenceAbstract: For compact Kaehler manifolds, Corlette and Simpson have established a nonabelian Hodge correspondence between representations of their fundamental groups and Higgs bundles on them subject to certain semistability conditions. Since the work of Faltings, analogy has been sought for p-adic rigid varieties. Inspired by the recent work of Heuer, we found that for a smooth rigid space over a perfectoid field, there is a natural etale Gm-gerbe on its cotangent bundle, whose coherent sheaf theory realizes a p-adic Simpson correspondence. This shows great similarity to results in prime characteristics discovered by Ogus-Vologodsky. In this talk, I will explain this perspective.This is joint work in progress with Bhargav Bhatt.