Leírás
Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined in terms of Tannakian duality of the category of vector bundles with (flat) connections on X. Morally, this is an algebraic version of the Riemann-Hilbert correspondence for curves. We investigate the equality between de Rham cohomology of a vector bundle with connection and the group cohomology of the corresponding representation of the differential fundamental group of X. The equality of the first and second cohomology groups is obvious. We show the equality of the higher cohomology groups. In particular we obtain the vanishing property for the cohomology groups of degree at least 3 of the differential fundamental group of a smooth projective curve. If time permits, I shall also discuss the case of smooth projective curves over a field of positive characteristic.
This is a joint work with Vo Quoc Bao and Dao Van Thinh (IM-VAST).
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