2017/06/20 by Rosenschon, Andreas, Sawant, Anand · 1 citation
#14C15 #14C25 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.1706.06386
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 étale 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.