p-adic Integration along the Hitchin Fibration and Applications
By Dimitry Wyss
By the work of Weil, Batyrev and Denef-Loeser one can use p-adic integration to compute the (stringy) number of rational points of a smooth or mildly singular algebraic variety X. One advantage of this approach is, that one can sometimes avoid the “bad locus” of X. We apply this idea to the moduli space M of G-Higgs bundles and obtain global invariants of M by considering only the generic fibers of the Hitchin fibration. For G = SLn, PGLn this gives a proof of the topological mirror symmetry conjecture of Hausel-Thaddeus. If time permits I will sketch for general G a connection with the geometric stabilization theorem of Ngˆo. This is joint work with Michael Groechenig and Paul Ziegler.