Homological algebra on an adams algebraic stack

Abstract

We will discuss joint work with Alonso Tarrío et al. (Expo Math 33:452– 501, 2015 [1]). We attach to a geometric stack a small non-trivial ringed site that has good functoriality properties when considering quasi-coherent sheaves. Our approach differs from (Various authors, Stacks Project [5]) in that they use big sites for which functoriality is obvious but not the existence of generators.