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arXiv · 1305.5690

The motivic Steenrod algebra in positive characteristic

Marc Hoyois·Shane Kelly·Paul Arne Østvær
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Abstract

Let S be an essentially smooth scheme over a field and l a prime number invertible on S. We show that the algebra of bistable operations in the mod l motivic cohomology of smooth S-schemes is generated by the motivic Steenrod operations. This was previously proved by Voevodsky for S a field of characteristic zero. We follow Voevodsky's proof but remove its dependence on characteristic zero by using étale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.

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Marc Hoyois, Shane Kelly, Paul Arne Østvær. 2013-07-31. The motivic Steenrod algebra in positive characteristic. https://arxiv.org/abs/1305.5690

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