Time: January 13, Monday, 16:00-17:00  

Venue: Lecture Hall

Title:  p-adic Simpson correspondence via gerbes

Speaker: Mingjia Zhang 张明嘉  (Princeton University)

Abstract: After the work of Corlette and Simpson on nonabelian Hodge theory for complex Kaehler manifolds, Faltings and Deninger-Werner initiated a search for an analogy for rigid spaces over p-adic fields. Recently, Heuer established such a correspondence for all smooth proper rigid spaces over algebraically closed fields, where the proetale site of a rigid space plays an important role. Inspired by his work, we observe that proetale vector bundles on a smooth rigid space over a perfectoid field can be interpreted as twisted sheaves on an etale G_m gerbe on its cotangent bundle. This gives a new perspective on the p-adic Simpson correspondence, leading to more general results. I will explain this perspective based on joint work in progress with Bhargav Bhatt.