Seminar

In the early 90s, Simpson established an equivalence between the category of local systems, and that of the semi-stable Higgs bundles whose Chern class is zero, over a smooth projective variety over the complex numbers. Such a correspondence between Higgs bundles and local systems is sometimes called the Simpson correspondence. In positive characteristic, an analogue of this result was first discovered by Ogus and Vologodsky in 2007, for bundles with nilpotent connections and Higgs fields. Later on, Groechenig, Chen and Zhu also established a full correspondence without the nilpotence conditions, for bundles over curves. In this talk, following the approach of Groechenig,  I will show that a full correspondence still holds for bundles over abelian varieties.