Let S be an essentially smooth scheme over a field and ℓ ≠D char S a prime number. 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 életale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.

The motivic Steenrod algebra in positive characteristic / M. Hoyois, S. Kelly, P.A. Oestvaer. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 19:12(2017), pp. 3813-3849. [10.4171/JEMS/754]

The motivic Steenrod algebra in positive characteristic

P.A. Oestvaer
2017

Abstract

Let S be an essentially smooth scheme over a field and ℓ ≠D char S a prime number. 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 életale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.
The motivic Steenrod algebra and its dual
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/860124
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