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Journal of the European Mathematical Society

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Volume 19, Issue 12, 2017, pp. 3813–3849
DOI: 10.4171/JEMS/754

Published online: 2017-11-20

The motivic Steenrod algebra in positive characteristic

Marc Hoyois[1], Shane Kelly[2] and Paul Arne Østvær[3]

(1) Massachusetts Institute of Technology, Cambridge, USA
(2) Tokyo Institute of Technology, Japan
(3) University of Oslo, Norway

Let $S$ be an essentially smooth scheme over a field and $\ell\neq\mathrm {char}\: S$ a prime number. We show that the algebra of bistable operations in the mod $\ell$ 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 etale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.

Keywords: The motivic Steenrod algebra and its dual

Hoyois Marc, Kelly Shane, Østvær Paul: The motivic Steenrod algebra in positive characteristic. J. Eur. Math. Soc. 19 (2017), 3813-3849. doi: 10.4171/JEMS/754