BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peter Schenzel (Institut für Informatik. Martin-Luther-Universit ät Halle-Wittenberg.) DTSTART:20210625T120000Z DTEND:20210625T130000Z DTSTAMP:20260423T020956Z UID:VCAS/88 DESCRIPTION:Title: Ne ws about Koszul and \\v{C}ech complexes: Another view at local cohomology and completion-I\nby Peter Schenzel (Institut für Informatik. Martin- Luther-Universität Halle-Wittenberg.) as part of IIT Bombay Virtual Commu tative Algebra Seminar\n\n\nAbstract\nIn the first part of the talk\, we p resent some elementary new facts about \nKoszul and \\v{C}ech complexes wi th respect to a single element. \nWe construct free resolutions of the \\v {C}ech complex for \na system of elements in a commutative ring. \n\nThis is used in order to construct quasi-isomorphisms \nbetween the \\v{C}ech complexes and certain Koszul complexes.\nThe free resolution of the \\v{Ce ch} complex is applied in order \nto find relations to the left derived fu nctors of the completion \nas a certain Koszul homology. \n\nThis material provides an elementary introduction to some of the results \nof the speak ers joint work with A.-M. Simon (see "Completion\, \\v{C}ech \nand local h omology and cohomology. Interactions between them. Springer Monograph\, \n 2018") as well as some further developments.\n\nOne focus is the study of weakly proregular sequences and of proregular \nsequences which provides a new insight for the local cohomology as well as the \nleft derived funct ors of the completion. Finally we shall present an \napplication to prisms in the sense of Bhatt and Scholze.\n LOCATION:https://researchseminars.org/talk/VCAS/88/ END:VEVENT END:VCALENDAR