| Résume | The six functor formalism over locally compact Hausdorff spaces was developed by Masaki Kashiwara and Pierre Schapira in the book "Sheaves on Manifolds": this is done in the context of derived categories of sheaves of R-modules, with R a ring. In this talk I will show that one can extend the whole formalism to non-necessarily hypercomplete sheaves with values in any stable bicomplete ∞-category equipped with a closed symmetric monoidal structure. At the end I will show how being able to work at this level of generality allows one to prove that, if f is a map which induces a locally contractible geometric morphism, then the exceptional pullack along f satisfies a formula which was previously known to hold only for topological submersions. |
