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arXiv · 1706.06386

Rost nilpotence and \'etale motivic cohomology

Andreas Rosenschon·Anand Sawant
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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 $0$.

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Andreas Rosenschon, Anand Sawant. 2017-06-20. Rost nilpotence and \'etale motivic cohomology. https://arxiv.org/abs/1706.06386

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