| Résume | About a decade ago, Schiffmann showed that the number of absolutely
indecomposable vector bundles of coprime rank and degree on a curve over
a finite field can be expressed (up to a power of q) in terms of the
number of stable Higgs bundles. This result was later reproved and
generalized by Dobrovolska–Ginzburg–Travkin.
In this talk, I will explain a generalization of these results to
principal G-bundles for a reductive group G, in joint work with Zhiwei
Yun. We relate the number of absolutely indecomposable G-bundles on a
curve X over a finite field to the cohomology of the moduli stack of
stable parabolic G-Higgs bundles on X. |
