2014/09/11 by Tsao-Hsien Chen, Chen, Tsao-Hsien
Mathematics · #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1409.3517
Let G be a simple complex group of adjoint type. In his unpublished work, Z. Yun associated to each θ-group (G0, \mathfrak g1) and a vector X∈\mathfrak g1 a flat G-connection ∇ X on \mathbb P1-\0,∞\, generalizing the construction of Frenkel and Gross in [FG]. In this paper we study the local monodromy of those flat G-connections and compute the de Rham cohomology of ∇X with values in the adjoint representations of G. In particular, we show that in many cases the connection ∇X is cohomologically rigid.