Résume | About 10 years ago, Schiffmann proved that the number of absolutely indecomposable vector bundles on a curve over a finite field (with degree coprime to the rank) is equal to the number of stable Higgs bundles of the same rank and degree (up to a power of q). Dobrovolska, Ginzburg and Travkin gave another proof of this result in a slightly different formulation, but neither proof generalizes in an obvious way to G-bundles for other reductive groups G.
In joint work with Zhiwei Yun, we generalize the above results to G-bundles. Namely, we express the number of absolutely indecomposable G-bundles on a curve X over a finite field in terms of the cohomology of the moduli stack of stable parabolic G-Higgs bundles on X. |