Dr. Morten Lüders (Hannover)

Abstract: We explain a joint work with Matthew Morrow on $p$-adic Milnor K-theory. Our main theorem is a comparison of mod $p^r$ Milnor K-groups of $p$-henselian local rings with the Milnor range of a nwly defined syntomic cohomology theory by Bhatt, Morrow and Scholze. We begin by putting our result into context. Then we sketch the proof which builds on an analysis of a filtration on Milnor K-groups and a new technique called the left Kan extension from smooth algebras.