Homology, Homotopy and Applications

Volume 10 (2008)

Number 3

Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson

Extended powers and Steenrod operations in algebraic geometry

Pages: 85 – 100

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n3.a5

Authors

Terrence Bisson (Department of Mathematics, Canisius College, Buffalo, New York, U.S.A.)

Aristide Tsemo (Collège Boréal, Toronto, Ontario, Canada)

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

14F43, 55N22, 55S05

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