Algebra/Topology Seminar 17122020

Speaker: Arpon Raksit

Title: q–de Rham cohomology and complex K-theory

Abstract: Work of Bhatt–Morrow–Scholze uncovered a "q-deformation" of de Rham cohomology in p-adic algebraic geometry, and moreover a striking relation of this invariant to stable homotopy theory via topological Hochschild homology, i.e. Hochschild homology relative to the sphere spectrum. I will discuss ongoing work concerning a related phenomenon involving Hochschild homology relative to the complex K-theory spectrum.