Abstract: I will review the strategy of the proof of the conservativity conjecture for the classical realisations of Voevodsky motives over a characteristic zero fields. I will also mention some other consequences of this proof such as the nilpotence of endomorphisms acting by zero on cohomology.
I will discuss main ideas and steps in the
proof of Milnor and Bloch-Kato Conjectures given by Voevodsky .
of anisotropy of an algebraic variety (that is, the absence of points of degree prime to a given p on it) plays an important role (most notably, in the theory of quadratic forms).