p-adic Milnor K-theory of p-adic rings

Abstract: Joint with Morten L\"uders. The Milnor K-theory of a local ring may initially appear to be an ad-hoc invariant, but turns out to be motivic in nature. In particular, Nesterenko and Suslin showed that the Milnor K-groups of a field were isomorphic to its motivic cohomology in the range where degree equals weight; by then proving the Beilinson----Lichtenbaum conjectures, Voevodsky connected motivic cohomology to l-adic \'etale cohomology and so established the Bloch---Kato conjecture. We will present p-adic analogues of these results by describing the p-adic Milnor K-theory of p-complete local rings in terms of the syntomic cohomology introduced by Bhatt---M.---Scholze.

commutative algebraalgebraic geometryalgebraic topologygeometric topologyK-theory and homology

Audience: researchers in the topic

electronic Algebraic K-theory Seminar

Series comments: Description: Research seminar on algebraic K-theory