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SUMMARY:${\\Bbb P}^1$-Localisation and a Possible Definition of Arithmetic
Kodaira-Spencer Classes
DTSTART;VALUE=DATE-TIME:20190424T083000Z
DTEND;VALUE=DATE-TIME:20190424T093000Z
DTSTAMP;VALUE=DATE-TIME:20200922T153550Z
UID:indico-event-4566@indico.math.cnrs.fr
DESCRIPTION:${\\mathbb A}^1$-localisation is a universal construction whic
h produces "cohomology theories" for which the affine line ${\\mathbb A}^1
$ is contractible. It plays a central role in the theory of motives à la
Morel-Voevodsky. In this talk\, I'll discuss the analogous construction wh
ere the affine line is replaced by the projective line ${\\mathbb P}^1$. T
his is the ${\\mathbb P}^1$-localisation which is arguably an unnatural co
nstruction since it produces "cohomology theories" for which the projectiv
e line ${\\mathbb P}^1$ is contractible. Nevertheless\, I'll explain a few
positive results and some computations around this construction which nat
urally lead to a definition of Kodaira-Spencer classes of arithmetic natur
e. (Unfortunately\, it is yet unclear if these classes are really interest
ing and nontrivial.)\n\nhttps://indico.math.cnrs.fr/event/4566/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4566/
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