BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jessica Fintzen (University of Bonn) DTSTART:20250924T220000Z DTEND:20250924T230000Z DTSTAMP:20260423T024730Z UID:UtahRTNT/1 DESCRIPTION:Title: Reduction to depth-zero for $\\bar{\\mathbb{Z}}[1/p]$-representations of p-adic groups\nby Jessica Fintzen (University of Bonn) as part of Univ ersity of Utah Representation Theory / Number Theory Seminar\n\nLecture he ld in LCB 222.\n\nAbstract\nThe category of smooth complex representations of p-adic groups decomposes into Bernstein blocks and by a joint result w ith Adler\, Mishra and Ohara from August 2024 we know that under some mino r tameness assumptions each Bernstein block is equivalent to a depth-zero Bernstein block\, which are the representations that correspond roughly to representations of finite group of Lie type. This result allows to reduce a lot of problems about representations of p-adic groups and the Langland s correspondence to their depth-zero counterpart that is often easier to s olve or already known. For number theoretic applications one likes to have a similar result when working with representations whose coefficients are a more general ring than the complex numbers. \n\nIn this talk we present analogous results for R-representations of p-adic groups where R is any r ing that contains all p-power roots of unity\, a fourth root of unity and the inverse of a square-root of p\, for example\, R could be a field of ch aracteristic different from p or the ring $\\bar{\\mathbb{Z}}[1/p]$. This is joint work in progress with Jean-François Dat. While the result is ana logous to the result with complex coefficients (except for the “blocks ” being “larger”)\, the proof is of a very different nature. In the complex setting the proof is achieved via type theory and an isomorphism o f Hecke algebras\, which are techniques not available for general R-repres entations. We will sketch in the talk how we deal with the category of R-r epresentations instead.\n LOCATION:https://researchseminars.org/talk/UtahRTNT/1/ END:VEVENT END:VCALENDAR