SMS scnews item created by Hannah Bryant at Thu 25 Nov 2021 1557
Type: Seminar
Modified: Thu 2 Dec 2021 1109
Distribution: World
Expiry: 2 Dec 2021
Calendar1: 2 Dec 2021 1500-1630
CalLoc1: Online via Zoom
Auth: (hbry8683) in SMS-SAML

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) 

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

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 

Other upcoming SMRI events can be found here:

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