Verdier duality on conically smooth stratified spaces

Volpe, Marco¹

¹Department of Mathematics, University of Toronto, Toronto, ON, Canada

Algebraic and Geometric Topology, Tome 25 (2025) no. 2, pp. 919-950

Résumé

We prove a duality for constructible sheaves on conically smooth stratified spaces. We consider sheaves with values in a stable and bicomplete ∞-category equipped with a closed symmetric monoidal structure, and in this setting constructible means locally constant along strata and with dualizable stalks. The crucial point where we need to employ the geometry of conically smooth structures is in showing that Lurie’s version of Verdier duality restricts to an equivalence between constructible sheaves and cosheaves: this requires a computation of the exit paths ∞-category of a compact stratified space, which we obtain via resolution of singularities.

Détail

DOI : 10.2140/agt.2025.25.919

Keywords: constructible sheaves, finite infinity categories, stratified spaces, conically smooth, Verdier duality, dualizing complex

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