Remy van Dobben de Bruyn (Universität Utrecht)

Abstract: Given two schemes S and S’, we show that any equivalence between Sch/S and Sch/S’ comes from a unique isomorphism between S and S’. In particular, the category of schemes does not have any nontrivial automorphisms. This eliminates all Noetherian and finite type hypotheses from a result of Mochizuki, and answers a series of questions of Brandenburg. The methods are analogous to those in anabelian geometry (but easier), and this talk also serves as an introduction to those ideas for non-experts.