Motifs et adjoints

Abstract

We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. Among various applications, one is a functorial construction of the "Tate-Safarevic motive" introduced in arXiv:1401.6847 [math.NT]. We also deduce a possible approach to Bloch's conjecture on surfaces, by reduction to curves.

arXiv commentin French. Minor changes; added Th. 8.6 to justify the terminology "Tate-Safarevic motive"; its proof will be completed elsewhere