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STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

Part of: Operations and obstructions Algebraic geometry: Foundations (Co)homology theory

Published online by Cambridge University Press:  04 May 2021

Federico Scavia Open the ORCID record for Federico Scavia [Opens in a new window]
Federico Scavia*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 Canada (scavia@math.ubc.ca)
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Abstract

Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Keywords

Stacksde Rham cohomologySteenrod operationscohomology operationsoperads

MSC classification

Primary: 14F40: de Rham cohomology
Secondary: 55S10: Steenrod algebra 14A20: Generalizations (algebraic spaces, stacks) 14F20: Étale and other Grothendieck topologies and (co)homologies
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 2 , March 2023 , pp. 493 - 540
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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