Emanuel Reinecke: Unipotent homotopy theory of schemes

Abstract

In this talk, I will present a notion of unipotent homotopy theory for schemes, which is based on Toën's work on affine stacks. I will discuss some general properties of the resulting unipotent homotopy group schemes and explain how over a field of characteristic p>0, they often recover the unipotent completion of the Nori fundamental group scheme, p-adic etale homotopy groups, and Artin–Mazur formal groups. As examples, we will see computations in the case of curves, abelian varieties, and Calabi–Yau varieties. Joint work with Shubhodip Mondal.