Frobenius generation for algebraic stacks

Abstract

We introduce a notion of $F$-finiteness for algebraic stacks in positive characteristic. Our main result shows that sufficiently many Frobenius pushforwards generate the bounded derived categories of coherent sheaves on Noetherian concentrated $F$-finite algebraic stacks with quasi-finite and separated diagonal. This generalizes, and independently recovers, a result of Ballard--Iyengar--Lank--Mukhopadhyay--Pollitz.

improved results, independent of BILMP