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]
|Titolo:||The motivic Steenrod algebra in positive characteristic|
|Parole Chiave:||The motivic Steenrod algebra and its dual|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4171/JEMS/754|
|Appare nelle tipologie:||01 - Articolo su periodico|