Guest lectures and seminars - Page 119

The advances on the Milnor- and Bloch-Kato conjectures have led to a good  understanding of motivic cohomology and algebraic K-theory with finite  coefficients.  However, important questions remain about rational motivic  cohomology and algebraic K-theory, including the Beilinson-Soulé vanishing  conjecture.  We discuss how the speaker's "connectivity conjecture" for  the stable rank filtration of algebraic K-theory leads to the construction  of chain complexes whose cohomology groups may compute rational motivic  cohomology, and simultaneously satisfy the vanishing conjecture.  These  "rank complexes" serve a similar purpose as Goncharov's candidates for  motivic complexes, but have the advantage that they have a precise  relation to rational algebraic K-theory.

The so-called Koras-Russell threefolds are a family of topologically

contractible rational smooth complex affine threefolds which played an

important role in the linearization problem for multiplicative group

actions on the affine 3-space. They are known to be all diffeomorphic to

the 6-dimensional Euclidean space, but it was shown by Makar-Limanov in

the nineties that none of them are algebraically isomorphic to the affine

3-space. It is however not known whether they are stably isomorphic or not

to an affine space. Recently, Hoyois, Krishna and Østvær proved that many

of these varieties become contractible in the unstable A^1-homotopy

category of Morel and Voevodsky after some finite suspension with the

pointed projective line. In this talk, I will explain how additional

geometric properties related to additive group actions on such varieties

allow to conclude that a large class of them are actually A^1-contractible

(Joint work with Jean Fasel, Université Grenoble-Alpes).

Digital signalbehandling og bildeanalyse, UiO and PGS

The effects of moving rough sea surfaces on seismic data.