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SUMMARY:Prismatic cohomology and a proof of Totaro's conjecture
DTSTART:20230403T120000Z
DTEND:20230403T130000Z
DTSTAMP:20260610T152500Z
UID:indico-event-9471@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry Kubrak (IHES)\n\nIn 2017\, in https://arxiv.o
 rg/abs/1703.03545\, Totaro initiated the study of de Rham cohomology of cl
 assifying stacks of reductive groups relating it to some purely representa
 tion-theoretic data via Hodge-to de Rham spectral sequence. He was able to
  explicitly identify de Rham cohomology with the singular cohomology in mo
 st examples and conjectured that at least an inequality of dimensions shou
 ld hold in general. I will talk about joint work https://arxiv.org/abs/210
 5.05319 with A.Prikhodko where among other things we proved this conjectur
 e using prismatic cohomology. I will discuss some particular examples as w
 ell as the general strategy of the proof. If time permits I will also brie
 fly talk about the results of our more recent paper https://arxiv.org/abs/
 2211.17227 where a version of rational Hodge theory was established for al
 l Artin stacks with a smooth d-Hodge-proper integral model. This implies s
 ome new results on crystallinity of etale cohomology in the schematic sett
 ing as well.\n\nhttps://indico.math.cnrs.fr/event/9471/
LOCATION:CMLS\, École Polytechnique
URL:https://indico.math.cnrs.fr/event/9471/
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