Algebra/Topology seminar-16122024

Speaker: Ferdinand Wagner 

Title: Refined TC^- over ku

Abstract: As a consequence of Efimov's proof of rigidity of the category of localising motives, Efimov and Scholze have constructed refinements of THH and TC^-. These refinements contain vastly more information than the original. For example, even for rational inputs, they usually contain non-trivial p-complete information, and already the refined THH of Q is a highly non-trivial object. In this talk I'll explain how to compute this object after base change to ku (joint work with Samuel Meyer). I'll also sketch an idea how use refined THH/TC^- to construct an interesting cohomology theory in arithmetic geometry.