Oratrices et orateurs et résumés > Werner Annette

This is joint work with Ben Heuer and Lucas Mann. For an abeloid variety A over a complete algebraically closed field extension K of the p-adic numbers, we construct an equivalence between finite-dimensional continuous K-linear representations of the Tate module and a certain subcategory of the Higgs bundles on A. To do so, our central object of study is the category of vector bundles for the v-topology on the diamond associated to A. We prove that any pro-finite-étale v-vector bundle can be built from pro-finite-étale v-line bundles and unipotent v-bundles.