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SUMMARY:Motivic cohomology of singular varieties - Matthew Morrow (Institu
 t de Mathématiques de Jussieu)
DTSTART:20220621T123000Z
DTEND:20220621T133000Z
UID:TALK174413@talks.cam.ac.uk
DESCRIPTION:I will given an overview of some joint work with Elden Elmanto
  in which we construct a non-A^1-invariant motivic cohomology theory for s
 chemes over fields. It is built by glueing A^1-invariant\, cdh-local\, mot
 ivic cohomology (developed in a separate project joint with Tom Bachmann a
 nd Elmanto) to contributions from either syntomic cohomology or derived de
  Rham cohomology. It satisfies various properties akin to classical motivi
 c cohomology\, such as an Atiyah&mdash\;Hirzebruch spectral sequence conve
 rging to algebraic K-theory\, the projective bundle formula\, some Beilins
 on&mdash\;Lichtenbaum type formulae\, and the degree 2d\, weight d motivic
  cohomology is related to zero cycles on singular varieties. But there are
  also new phenomena motivated by the structure of algebraic K-theory\; for
  example\, it has a vanishing range which refines Weibel&rsquo\;s vanishin
 g conjecture and satisfies pro-cdh descent.
LOCATION:Seminar Room 1\, Newton Institute
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