Rost nilpotence and etale motivic cohomology

Rosenschon, Andreas; Sawant, Anand (2018): Rost nilpotence and etale motivic cohomology. In: Advances in Mathematics, Vol. 330: pp. 420-432

Abstract

A smooth projective scheme X over a field k is said to satisfy the Rost nilpotence principle if any endomorphism of X in the category of Chow motives that vanishes on an extension of the base field k is nilpotent. We show that an etale motivic analogue of the Rost nilpotence principle holds for all smooth projective schemes over a perfect field. This provides a new approach to the question of Rost nilpotence and allows us to obtain an elegant proof of Rost nilpotence for surfaces, as well as for birationally ruled threefolds over a field of characteristic 0.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0001-8708
• Language: English