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Sydney Mathematical Research Institute

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SMRI Algebra and Geometry Online

'Blowup formulas for nilpotent sensitive cohomology theories' Shane Kelly (Tokyo Institute of Technology)

Thursday 2nd December 3:00pm-4:30pm (AEDT) Register:

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.

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