published on February 23, 2026
Illustration in Mathematics and CS — Made Broadly Accessible by AI: From Opportunity to Practice
By Erika Berenice Roldan Roa
Prismatic and syntomic cohomology of ring spectra
By Jeremy Hahn
Appears in collection : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs
I will explain a construction of the motivic filtration on the topological cyclic homology of ring spectra, generalizing work of Bhatt–Morrow–Scholze and Bhatt–Lurie on the topological cyclic homology of discrete rings. This is joint with Arpon Raksit and Dylan Wilson. As time permits, I will discuss works in progress using the motivic spectral sequence to obtain new calculations in algebraic $K$-theory and prove higher chromatic variants of local Tate duality.
