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SMRI Algebra and Geometry Online: Kelly 'Blowup formulas for nilpotent sensitive cohomology theories'
SMRI Algebra and Geometry Online
'Blowup formulas for nilpotent sensitive cohomology theories'
Shane Kelly (Tokyo Institute of Technology)

Abstract: This is joint work in progress with Shuji Saito. Many cohomology theories of interest (l-adic cohomology, de Rham cohomology, motivic cohomology, K-theory...) have long exact sequences associated to blowups. Such a property can be neatly encoded in a Grothendieck topology such as the cdh-topology or the h-topology. These topologies appeared in Voevodsky's proof of the Bloch-Kato conjecture, and more recently in Beilinson's simple proof of Fontaine's CdR conjecture, and in Bhatt and Scholze's work on projectivity of the affine Grassmanian.

A feature of these topologies which often turns out to be a bug is that the associated sheaves cannot see nilpotents. In this talk I will discuss a modification which can see nilpotents, and which still has long exact sequences for many blowups.

Biography: Shane Kelly is an Associate Professor at Tokyo Institute of Technology. His research area is algebraic K-theory and motivic homotopy theory, and more recently he is interested in applications to representation theory. His graduate studies were mostly based in Paris; in 2012 he received a PhD jointly from Université Sorbonne Paris Nord and The Australian National University under the joint supervision of Cisinski and Neeman, respectively.


Note
These seminars will be recorded, including participant questions (participants only when asking questions), and most will be uploaded to the SMRI YouTube Channel https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

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Dec 2, 2021 03:00 PM in Canberra, Melbourne, Sydney

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