Counting absolutely indecomposable G-bundles

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Konstantin Jakob (TU Darmstadt)

Time：

Fri., 15:30-16:30, Mar. 14, 2025

Venue：

B626, Shuangqing Complex Building A

Title:

Counting absolutely indecomposable G-bundles

Abstract：

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.