Bruno Kahn

Abstract:We construct an isomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties (or more general sheaves) over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective...

I will give the definition of birational motives and explain how they can be used in various areas of algebraic geometry: counting rational points over finite fields, defining the "Tate-Shafarevich motive" of an abelian variety over a function field...