Fabio Tonini: Representations of the Nori fundamental group and variants

Abstract: The Nori fundamental group scheme of a scheme X is a profinite group scheme that "controls" torsors over X under finite group schemes.

In the talk I will describe its category of representations by considering vector bundles with extra structure. I will also talk about a variant of this group, the local fundamental group scheme.

In the first part I will recall some notions about group schemes, torsors and Tannaka duality.