Trace methods for K-theory of stable infinity-categories (Victor Saunier)

Orateur : Victor Saunier (Université Paris 13)

Lieu : salle des Séminaires M3

Résumé :

K-theory is a very important yet very mysterious invariant of rings, and most of its computations go through the heavy machinery of trace methods which relates K-theory to various flavours of topological Hochschild homology. The goal of this talk is to recast the story of trace methods in the world of stable infinity-categories, first gently explaining how to define K-theory in this setting following Blumberg-Gepner-Tabuada and then how to use these ideas to generalize, simplify and explain many aspects of trace methods. Part of this is joint work with Yonatan Harpaz and Thomas Nikolaus.