A fundamental group for schemes in mixed characteristic

11.12.2018 13:15 - 14:45

Joao-Pedro Dos Santos, Institut de Mathématiques de Jussieu - Paris Rive Gauche

Abstract: Determining unramifed coverings over various base spaces is a classical activity, which can take place in many contexts: topological, analytic, algebraic or arithmetic. In this talk I shall report on a theory proposed by myself and P. H. Hai accounting for the case of finite principal bundles (analogues of unramified coverings) over projective schemes in mixed characteristic.    

In the first part of the talk, after a brief review of classical theories, I shall explain the method of constructing pro-algebraic groups (or affine group schemes) from tensor categories defined over a field or a Dedekind ring. I will then move on to show how these can be applied to classify principal bundles over algebraic varieties following theories of Nori and others. 

In the second part I will focus on the case of schemes defined over a complete DVR. After introducing the fundamental groups in question, I will explain how to interpret them from internal data of the base.  


H. Grobner, A. Minguez-Espallargas, A. Mellit


SR 01, EG, OMP 1