Algebra/Topology seminar

Speaker: Gabriel Angelini-Knoll

Title: Syntomic cohomology of regular ring spectra

Abstract: Work of Hahn and Wilson demonstrated that many qualitative questions about algebraic K-theory and the arithmetic of ring spectra can be answered using a suitable filtration of topological cyclic homology, which closely approximates algebraic K-theory. Together with Raksit, they later observed that this filtration fits into a general paradigm, which also recovers filtrations previously studied by Bhatt—Morrow—Scholze, Antieau, Morin, and Bhatt—Lurie. I will report on some applications of this technology to regular ring spectra such as real topological K-theory, connective Morava K-theory, truncated Brown-Peterson spectra, and topological modular forms. Each of these projects is based on joint work with some subset of my collaborators Ausoni, Rognes, Hahn, Wilson, Bruner, Davies, and Yang.