Algebra/Topology Seminar

Speaker: Shubhodip Mondal

Title: Unipotent homotopy theory of algebraic varieties

Abstract: Building on Toen's work on higher (affine) stacks, I will discuss a notion of homotopy theory for algebraic varieties, which we call "unipotent homotopy theory". Over a field of characteristic p>0, I will explain how our unipotent homotopy group schemes recover (1) unipotent completion of the Nori fundamental group scheme, (2) p-adic étale homotopy groups, and (3) certain formal group laws arising from algebraic varieties constructed by Artin--Mazur. Time permitting, I will discuss unipotent homotopy types of Calabi--Yau varieties and show that the unipotent homotopy group schemes πUi of Calabi--Yau varieties (of dimension n) are derived invariant for all i; the case i = n corresponds to a recent result of Antieau--Bragg. Joint work with Emanuel Reinecke (in progress).