Frobenius generation for algebraic stacks

Abstract

This work investigates the Frobenius morphism on derived categories associated with algebraic stacks in positive characteristic. Particularly, we show that in many cases sufficiently many Frobenius pushforwards of a compact generator produce a classical or strong generator for the bounded derived category of coherent sheaves. In the case of Deligne--Mumford stacks, we can bound the number of iterates required.