Algebra/Topology Seminar

Speaker: Matteo Tamiozzo

Title: The tame Hilbert symbol and central extensions in mixed characteristic

Abstract: Arbarello-De Concini-Kac developed in the 80s an approach to the Weil reciprocity law over function fields based on a description of tame symbols via central extensions constructed using the determinant bundle on an infinite-dimensional Grassmannian. After reviewing this, I will discuss how to construct analogous central extensions in mixed characteristic, using determinants of finite sets with an action of roots of unity (introduced by Kapranov-Smirnov). This also yields a K-theoretic interpretation of tame Hilbert symbols.