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) 
Register:
https://uni-sydney.zoom.us/meeting/register/tZIpd-yrqTgiGNUmqRgkI8-aAMHiHP9TfmLc

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 

Other upcoming SMRI events can be found here:
https://mathematical-research-institute.sydney.edu.au/news-events/