An effective criterion for finite monodromy of $\ell$-adic sheaves

TL;DR

This paper presents an effective criterion to determine when the monodromy group of certain $ ext{l}$-adic sheaves over finite fields is finite, based on their numerical complexity, improving previous theoretical results.

Contribution

The authors develop an explicit, effective criterion for finiteness of monodromy groups of $ ext{l}$-adic sheaves, extending Katz's earlier theoretical criterion with practical computability.

Findings

Provides an explicit bound for monodromy finiteness based on sheaf complexity

Extends Katz's criterion to an effective version with numerical parameters

Applicable to pure $ ext{l}$-adic sheaves on normal varieties over finite fields

Abstract

We provide an effective version of Katz' criterion for finiteness of the monodromy group of a lisse, pure of weight zero, $\ell$-adic sheaf on a normal variety over a finite field, depending on the numerical complexity of the sheaf