Eric Ahlqvist: Derived Stacks

This is the tenth talk of the seminar on algebraic K-theory and derived algebraic geometry . 

The seminar will be held via Zoom. 

Abstract

The goal of this talk is to define algebraic derived stacks and quasi-coherent sheaves on such. We will recall the notion of the cotangent complex of a morphism of simplicial commutative rings and define flat, étale and smooth morphisms of simplicial commutative rings. Derived stacks will be defined as sheaves of infinity groupoids for the étale topology on sRing. Then we define n-algebraicity by the usual inductive procedure.