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SUMMARY:Prismatic cohomology and a proof of Totaro's conjecture
DTSTART;VALUE=DATE-TIME:20230403T120000Z
DTEND;VALUE=DATE-TIME:20230403T130000Z
DTSTAMP;VALUE=DATE-TIME:20230605T092800Z
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\, Ă‰cole Polytechnique
URL:https://indico.math.cnrs.fr/event/9471/
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