Non-abelian Grothendieck Duality
Johns Hopkins University, U.S.A.
Duality is an endofunctor on a category inducing a self-equivalence, usually obtained by hom-ing into a certain dualizing object in the category. For example, in the category of finite dimensional vector spaces over a field $k$ the functor $V \longrightarrow Hom(V,k)$ is a dualizing functor, the vector space $k$ being the dualizing object.
More interesting examples include Serre duality for projective varieties over algebraically closed fields and Poincare duality for smooth closed orientable manifolds. Grothendieck vastly generalizes these classical examples by solving the problem of finding a dualizing complex in the derived category of any abelian category. We shall attempt to generalize this to homotopy categories of certain stable model categories. This will give us duality theorems for a larger class of objects, in particular, derived algebraic stacks.