Аннотация:
In the motivic homotopy theory one associates to a scheme X the socalled motivic stable homotopy category SH(X) that is a tensor triangulated category and is a universal source of cohomological invariants that are A^1-invariant
and satisfy descent in the Nisnevich topology. Motivic Adams conjecture provides
a partial information on the Picard group of SH(X). Every vector bundle over X gives
rise to an element in the Picard group of SH(X) via the Thom spectrum construction
and this yields a homomorphism from the Grothendieck group of vector bundles
over X to the Picard group of SH(X). Motivic Adams conjecture claims that the difference between the Thom space of a vector bundle and the Thom space of the
value of the k-th Adams operation on the vector bundle in Pic(SH(X)) is k-torsion. In
my talk I will introduce all this notions and give an outline of the proof for this conjecture. The talk is based on the work in progress joint with Elden Elmanto, Oliver
Roendigs and Maria Yakerson.