Seminar Arithmetic Geometry

Simon Pepin Lehalleur (Radboud-Universiteit Nijmegen)

Abstract: (Joint with Victoria Hoskins, Nijmegen) Moduli spaces and stacks of bundles on smooth projective curves are basic objects of algebraic geometry and part of the geometric set-up of the Langlands program for function fields. Their cohomology is well understood in some ways and still very mysterious in others. After some recollections on Voevodsky
motives, I will present several results about the motives of the moduli stack of vector bundles and the moduli spaces of semistable Higgs bundles, expressing them in terms of the motives of powers of the base curve. I will then explain how this can combined with constructions of Maulik-Shen to prove a motivic version of the “topological mirror symmetry” connecting moduli spaces of SL_n and PGL_n-Higgs bundles.

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