Speaker:  Toni Annala (Institute for Advanced Study)   

Title:  Atiyah duality and applications  

Abstract:  In topology, Atiyah duality provides a geometric model for the dual of the suspension spectrum of a smooth manifold. In this talk, we export this into algebraic geometry by proving an analogous claim in the non-A¹-invariant stable motivic homotopy theory of Annala-Hoyois-Iwasa. Besides recovering many Poincare duality type results, it has other surprising consequences. I will explain how to use the so-called A¹-colocalization functor to prove the independence of logarithmic cohomology theories from the choice of good compactification (without assuming resolution of singularities).