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

Owen Barrett
Vol. 6 (2024), No. 4, 703–734
DOI: 10.2140/tunis.2024.6.703
Abstract

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

Keywords
singular support, constructible sheaf, $\ell$-adic sheaf, universal local acyclicity, rational coefficients
Mathematical Subject Classification
Primary: 14F08, 14F20, 14F45, 14G17
Milestones
Received: 2 December 2023
Revised: 25 April 2024
Accepted: 10 May 2024
Published: 18 December 2024
Authors
Owen Barrett
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).