The singular support of an $\ell$-adic sheaf

TL;DR

This paper introduces a new definition of the singular support for $ ext{ell}$-adic sheaves on smooth varieties, combining existing theories to extend the concept to more general settings.

Contribution

It provides the first comprehensive definition of singular support for $ ext{ell}$-adic sheaves over any field, integrating Beilinson's and Hansen-Scholze's frameworks.

Findings

Defines singular support for $ ext{ell}$-adic sheaves on smooth varieties.

Combines Beilinson's and Hansen-Scholze's theories.

Extends the concept of singular support to broader contexts.

Abstract

We define the singular support of an $\ell$-adic sheaf on a smooth variety over any field. To do this, we combine Beilinson's construction of the singular support for torsion \'etale sheaves with Hansen and Scholze's theory of universal local acyclicity for $\ell$-adic sheaves.