Cohomology of the differential fundamental group of algebraic curves

2025/03/25 by Bao, Vo Quoc, Hai, Phung Ho, Van Thinh, Dao · 2 citations
#14F40 #14F43 #14L15 #18G15 #18G40 #18M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.19695

Abstract

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates the relationship between the de Rham cohomology of a vector bundle with connection and the group cohomology of the corresponding representation of the differential fundamental group of X . Consequently, we obtain some vanishing and non-vanishing results for the group cohomology.

Cited by

• On iterated universal extensions and Nori's fundamental group of nilpotent bundles
• Cohomology of the stratified fundamental group of curves

Related

• Connections on trivial vector bundles over projective schemes
• Cohomology of the stratified fundamental group of curves
• Differential Borel equivariant cohomology via connections
• The fundamental group of a noncommutative space
• Representations attached to vector bundles on curves over finite and p-adic fields, a comparison