Marco Artusa

I am interested in duality theorems in arithmetics, and in their possible formulation as Pontryagin duality. Condensed Mathematics plays a key role in this topic, since it allows to give topological structures to algebraic invariants appearing in Arithmetic Geometry, e.g. cohomology groups.

In particular, during my Ph.D. I built a topological/condensed cohomology theory for the Weil group of a p-adic field. Then, I used it to extend two classical duality results by Tate (the local Tate duality and the Tate duality for abelian varieties) giving them a topological flavour. These extended dualities take the form of a Pontryagin duality between locally compact abelian groups of finite ranks.