Matthew Morrow: Some recent developments in p-adic motivic cohomology (Part 1)

These talks will present an overview of recent work in p-adic étale motivic cohomology, in finite and mixed characteristic, due to various collaborations of Antieau, Bhatt, Clausen, Kelly, Lüders, Mathew, Nikolaus, Scholze, the speaker… We will introduce the motivic filtration on topological cyclic homology, whose graded pieces provide a general theory of p-adic étale motivic cohomology, and discuss its finer properties, comparisons to existing invariants, and prismatic interpretation. Along the way we will see concrete applications, such as to calculations of K-groups.