Number Theory Seminar

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