Équations différentielles motiviques et au–delà
# Spectral data for higher direct images of parabolic Higgs bundles

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#### IHP

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Description

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

professeur