Effective calculation of fundamental group schemes

Time: 9:30 -- 11:00, April 03, 2024.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: One of the drawbacks of the theory of algebraic fundamental groups, or group schemes, is that their calculation turns out to be quite difficult in general. Indeed, although there are many instances where one can assure that these group schemes are trivial, or at least small, it is far from being an easy task to find actual descriptions of these. This work wishes to contribute to the question by analysing the Nori fundamental group scheme of non-normal schemes by using the method of pinching. The computation leads us to the consideration of a class of co-commutative Hopf algebras in positive characteristic. It turns out that not much is known about this class of Hopf algebras either. This is a joint work (in progress) with J.P. dos Santos (Montpellier).