- journal article metadata
European Mathematical Society Publishing House
2017-11-23 23:40:01
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
19
2017
12
The motivic Steenrod algebra in positive characteristic
Marc
Hoyois
Massachusetts Institute of Technology, Cambridge, USA
Shane
Kelly
Tokyo Institute of Technology, Japan
Paul
Østvær
University of Oslo, Norway
The motivic Steenrod algebra and its dual
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.
Algebraic geometry
$K$-theory
3813
3849
10.4171/JEMS/754
http://www.ems-ph.org/doi/10.4171/JEMS/754
11
20
2017