A short proof of Rost nilpotence via refined correspondences
type: Item
instance of: scholarly article
title: A short proof of Rost nilpotence via refined correspondences
zbMATH Open document ID: 1044.11017
author: Patrick Brosnan
published in: Documenta Mathematica
publication date: 2003-09-24T00:00:00Z
full work available at URL: https://eudml.org/doc/123727
full work available at URL: 04.html
review text: 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.
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 11E04
zbMATH DE Number: 1985399
zbMATH Keywords: quadratic forms
zbMATH Keywords: correspondence
zbMATH Keywords: Chow groups and motives
reviewed by: Kazimierz Szymiczek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1985399