Fabrizio Andreatta

Abstract:

Following Faltings, I will describe the p-dic Simpson correspondence for 1-dimensional representations of the geometric fundamenta group of a curve over a p-adic local field, assuming that the curve has good reduction. Using the work of Deninger-Werner, I will show that every line bundle of degree 0 is in the image of the correspondence. I will briefly discuss the case of higher dimensional representations trying to relate the geometric point of view of Deninger-Werner with Faltings' point of view (via almost étale theory).