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Étale Chern Classes at the Prime 2

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Algebraic K-Theory and Algebraic Topology

Part of the book series: NATO ASI Series ((ASIC,volume 407))

Abstract

Let A be a commutative ring and q a power of 2. We investigate the étale Chern classes

$${c_{ik}}:{K_n}\left( {A;{\Bbb Z}/q} \right) \to H_{et}^k\left( {A;\mu _q^{ \otimes i}} \right)$$

which are defined whenever i ≥ 1 and n + k = 2i. These are group homomorphisms except when n = 2 and q is even. The usual product formula for c ik ({a,b}) remains valid, except when q = 2 and i ≥ 3, when there is a correction term.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Charles Weibel

Authors
  1. Charles Weibel
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Editor information

Editors and Affiliations

  1. Mathematics Department, University of Washington, Seattle, Washington, USA

    P. G. Goerss

  2. Mathematics Department, University of Western Ontario, London, Ontario, Canada

    J. F. Jardine

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© 1993 Springer Science+Business Media Dordrecht

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Weibel, C. (1993). Étale Chern Classes at the Prime 2. In: Goerss, P.G., Jardine, J.F. (eds) Algebraic K-Theory and Algebraic Topology. NATO ASI Series, vol 407. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0695-7_14

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  • DOI: https://doi.org/10.1007/978-94-017-0695-7_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4302-3

  • Online ISBN: 978-94-017-0695-7

  • eBook Packages: Springer Book Archive

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