Verdier duality on conically smooth stratified spaces

par Marco Volpe (MPIM Bonn)

mardi 6 déc. 2022, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

Verdier duality is a key feature of derived categories of constructible sheaves on well-behaved stratified spaces. In this talk we will explain how to extend the duality theorem to constructible sheaves on conically smooth stratified spaces and with values in a general stable bicomplete infinity-category. Our proof relies on two main ingredients, one categorical and one geometric. The first one is an equivalence between sheaves and cosheaves proven by Lurie in Higher Algebra. Lurie's theorem will appear in our discussion both as a fundamental building block for the six functor formalism in a very general setting and as a factor of the duality functor on constructible sheaves. The second is the unzip construction introduced by Ayala, Francis and Tanaka, which provides a functorial resolution of singularities to smooth manifolds with corners. This will be used to prove that the exit path infinity-category of any compact conically smooth stratified space is finite.