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Torsion Algebraic Cycles on Varieties Over Local Fields

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Algebraic K-Theory: Connections with Geometry and Topology

Part of the book series: NATO ASI Series ((ASIC,volume 279))

Abstract

In this article we study the torsion in the second Chow group of a smooth, projective scheme over a Henselian discrete valuation ring with finite or separably closed residue field. We show that the prime to p torsion of this group injects into the prime to p torsion of the special fibre (where p is the characteristic of the residue field). Using this result, we prove the finiteness of the prime to p torsion in the second Chow group of certain varieties over p-adic fields. We also prove similar results for other K-cohomology groups.

Research supported in part by the National Science Foundation

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Wayne Raskind

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  1. Wayne Raskind
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Editors and Affiliations

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

    J. F. Jardine

  2. Mathematics Department, McMaster University, Hamilton, Ontario, Canada

    V. P. Snaith

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© 1989 Kluwer Academic Publishers

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Raskind, W. (1989). Torsion Algebraic Cycles on Varieties Over Local Fields. In: Jardine, J.F., Snaith, V.P. (eds) Algebraic K-Theory: Connections with Geometry and Topology. NATO ASI Series, vol 279. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2399-7_12

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  • DOI: https://doi.org/10.1007/978-94-009-2399-7_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7580-0

  • Online ISBN: 978-94-009-2399-7

  • eBook Packages: Springer Book Archive

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