Lisse extensions of weaves

2025/01/07 by Adeel A. Khan, Khan, Adeel A. · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2501.04114

openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothendieck's six operations: more precisely, the lisse extension of a weave on schemes determines a weave on (higher) Artin stacks. The setup is general enough to apply to the stable motivic homotopy category with the six functor formalism of Voevodsky-Ayoub-Cisinski-Deglise, for instance, and is not specific to algebraic geometry: for example, it also applies to sheaves of spectra on topological stacks.

Cited by

• Abel maps for integral curves via a derived perspective

Related

• The six operations for sheaves on Artin stacks I: Finite Coefficients
• Formality for algebroid stacks
• The pro-étale topology for schemes
• The six operations for sheaves on Artin stacks II: Adic Coefficients
• Enhanced six operations and base change theorem for higher Artin stacks