A short proof of Rost nilpotence via refined correspondences
Let \(k\) be a field and \(\bar{k}\) its algebraic closure. Rost's nilpotence theorem asserts that an endomorphism of the integral Chow motive of a smooth quadric over \(k\) is nilpotent provided it becomes the zero endomorphism for the motive of the extended quadric over \(\bar{k}\). This result plays a role in a construction of the Rost motive which is essential to Voevodsky's proof of the Milnor conjecture. The author gives a new proof of the nilpotence theorem using a generalized notion of composition of algebraic correspondences. The author's general version of composition of Chow correspondences requires only that one of the three involved schemes be smooth and proper, the others can be arbitrary. Reviewer's remark: This is a truly highbrow mathematics where such concepts as schemes, motives, Chow correspondences and advanced intersection theory are taken for granted. It is amusing to notice that the only background definition the author gives is that of the hyperbolic plane.
scientific article; zbMATH DE number 1985399