Homology, Homotopy and Applications

Extended powers and Steenrod operations in algebraic geometry

Terrence Bisson and Aristide Tsemo

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Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. We adapt the methods used by Bisson-Joyal in studying Steenrod and Dyer-Lashof operations in unoriented cobordism and mod 2 cohomology.

Article information

Homology Homotopy Appl., Volume 10, Number 3 (2008), 85-100.

First available in Project Euclid: 1 September 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 55S05: Primary cohomology operations

Extended power functors Steenrod operations algebraic geometry cohomology unoriented cobordism formal group law $Q$-ring


Bisson, Terrence; Tsemo, Aristide. Extended powers and Steenrod operations in algebraic geometry. Homology Homotopy Appl. 10 (2008), no. 3, 85--100. https://projecteuclid.org/euclid.hha/1251832468

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