The motivic Steenrod algebra in positive characteristic

By Marc Hoyois, Shane Kelly, P. Ostvaer. 2013

89 citations recorded by the source corpus.

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 etale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26053835f272b7f2a9a7ac1fc4546edf3449e57b

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Citations in the corpus

Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, methodology): “Because of the special form the slices of KQ and KT have, this involves the motivic Steenrod squares Sq constructed by Voevodsky [61] and further elaborated on in Hoyois, Kelly and Østvær [18].”
Integral mixed motives in equal characteristic (2014, methodology): “This was recently generalized to perfect fields of characteristic p > 0, up to inverting p, by Hoyois, Kelly and Østvær, [HKØ13].”
The first stable homotopy groups of motivic spheres (2016, methodology): “It allows us to calculate differentials using the action of the motivic Steenrod algebra on motivic cohomology groups [28], [75].”