Abstract

The goal of this talk is to explain how to extend Grassmannians to the world of derived stacks, i.e. how to construct a satisfying derived enhancement of Grassmannian varieties. I will begin by discussing some background about derived geometric stacks and in particular I will focus on Artin-Lurie-Pridham representability theorem, which provides us with a “computational” criterion to check whether a simplicial presheaf of derived algebras is a derived geometric stack. Then I will use such a result in order to study derived moduli of perfect complexes and filtered perfect complexes over a base scheme; finally the derived Grassmannian will arise as some suitable homotopy limit of such stacks. Time permitting I will end by sketching how to use this derived version of the Grassmannian to obtain a derived version of Griffiths’ period mapping.