BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthew Morrow (Jussieu) DTSTART:20201201T170000Z DTEND:20201201T180000Z DTSTAMP:20260423T021420Z UID:eAKTS/11 DESCRIPTION:Title: p -adic Milnor K-theory of p-adic rings\nby Matthew Morrow (Jussieu) as part of electronic Algebraic K-theory Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nJoint with Morten L\\"uders. The Milnor K-theory of a l ocal ring may initially appear to be an ad-hoc invariant\, but turns out t o be motivic in nature. In particular\, Nesterenko and Suslin showed that the Milnor K-groups of a field were isomorphic to its motivic cohomology i n 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 wi ll present p-adic analogues of these results by describing the p-adic Miln or K-theory of p-complete local rings in terms of the syntomic cohomology introduced by Bhatt---M.---Scholze.\n LOCATION:https://researchseminars.org/talk/eAKTS/11/ END:VEVENT END:VCALENDAR