Higgs26: On Fourier-Mukai transforms for Hitchin systemsWorkshop
by
Endenicher Allee 60, R. 0.008
Mathezentrum
In this talk we consider the moduli stack of (possibly meromorphic) semistable (GL_r)-Higgs bundles on a curve. The Dolbeault Langlands conjecture of Donagi-Pantev (later refined by Padurariu-Toda) predicts roughly the existence of an autoequivalence of the derived category of coherent sheaves on this moduli stack, which is compatible with certain classical limit Hecke and Wilson operators. In 2006, Donagi and Pantev further proposed that the kernel for such an autoequivalence may be constructed as a degeneration of the usual Poincare sheaf for Jacobians of spectral curves. In this talk we present some evidence for these conjectures, and some interactions of this equivalence with the obvious G_m-action on the moduli stack of Higgs bundles.