Drinfeld's lemma for algebraic stacks

TL;DR

This paper extends Drinfeld's lemma, a key result for splitting local systems over schemes, to the broader context of algebraic stacks, enhancing its applicability in algebraic geometry.

Contribution

The paper proves that Drinfeld's lemma applies to algebraic stacks, generalizing a fundamental splitting result from schemes to stacks.

Findings

Drinfeld's lemma holds for algebraic stacks.

The extension broadens the scope of local system analysis.

Implications for the study of algebraic stacks and local systems.

Abstract

Drinfeld's lemma is a powerful tool for splitting $\ell$-adic local systems defined over a product of connected schemes over a finite field. In this paper, we show that Drinfeld's lemma also holds true for algebraic stacks.