Research-Parallel transport for Higgs bundles over p-adic curves

Research

All

Parallel transport for Higgs bundles over p-adic curves

Speaker: Daxin Xu (Morningside Center of Mathematics, AMSS)
Time: Mar 11, 2022, 10:30-11:30
Location: Zoom ID 5581187360, Passcode sustech123

Abstract

Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric \'etale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree zero over X. We will talk about an equivalence between these representations and Higgs bundles, which potentially admit a strongly semi-stable of degree zero reduction for their underlying vector bundle. These Higgs bundles are semi-stable of degree zero and we will investigate some evidences for Faltings' conjecture