Équations différentielles motiviques et au–delà

Spectral data for higher direct images of parabolic Higgs bundles

by Prof. Carlos Simpson (CNRS, Université de Nice)



11, rue Pierre et Marie Curie

Mochizuki's Kobayashi-Hitchin correspondence allows us to represent local systems on 
quasiprojective varieties by parabolic logarithmic Higgs bundles. The Sabbah-Mochizuki
theory generalizing Saito's mixed Hodge modules then provides a framework for the 6-functor 
formalism on these objects. However, this setup involves working with lambda-connections for
all values of lambda. In our work with Donagi and Pantev, we made explicit the 
formula for the higher direct image, looking solely at the Dolbeault fiber (lambda = 0) of 
Higgs bundles. In generic cases this yields a nice formula for the spectral variety
of the higher direct image Higgs bundle. We'll then look at how this applies to the
question of calculating Hecke correspondences in the Donagi-Pantev program for constructing
Hecke eigensheaves in geometric Langlands.

Organized by

V. Roubtsov