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SUMMARY:Splitting vector bundles on smooth real affine varieties
DTSTART:20260415T120000Z
DTEND:20260415T132000Z
DTSTAMP:20260411T202100Z
UID:indico-event-16440@indico.math.cnrs.fr
DESCRIPTION:Speakers: Samuel Lerbet (ENS)\n\n \nLet X be a smooth affine 
 variety over a perfect field k. A natural question regarding vector bundle
 s on X is when they split a trivial rank 1 summand\; this question is rela
 ted to the comparison between vector bundles and K-theory classes. When k 
 is algebraically closed of characteristic 0\, the splitting of a trivial t
 ank 1 summand for vector bundles of large rank in the unstable range\, nam
 ely of corank at most 1 where the corank is the difference between the dim
 ension and the rank\, is entirely governed by the vanishing of the top Che
 rn class: this is the confirmation of Murthy's conjecture by Asok–Bachma
 nn–Hopkins\, building on ideas of Asok–Fasel. When k has more arithmet
 ic complexity\, this result usually fails\, but motivic homotopy theory pr
 ovides a systematic way of approaching the splitting problem in this gener
 ality. We will compare this motivic approach to topology over the real loc
 us of the variety under consideration in the specific case where k is the 
 field of real numbers\, for which the arithmetic is as simple as possible\
 , in search for a real Murthy's conjecture. This is joint work with Aravin
 d Asok and Jean Fasel.\n\nhttps://indico.math.cnrs.fr/event/16440/
LOCATION:Salle Pierre Grisvard (Institut Henri Poincaré)
URL:https://indico.math.cnrs.fr/event/16440/
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