New York Journal of Mathematics
Volume 14 (2008) 225-233

Volume 14

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Ján Mináč, Andrew Schultz, and John Swallow

Galois module structure of Milnor K-theory mod ps in characteristic p

Published: June 23, 2008
Keywords: Milnor K-theory, cyclic extension, Galois module, norm
Subject: 19D45, 12F10
Abstract
Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s∈ N, we determine KmE/psKmE as a (Z/psZ) [Gal(E/F)]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero.
Acknowledgements

The first author's research was supported in part by NSERC grant R0370A01, and by a Distinguished Research Professorship at the University of Western Ontario. He was also supported by the Mathematical Sciences Research Institute, Berkeley.
The third author's research was supported in part by NSF grant DMS-0600122.
Author information

Ján Mináč:
Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario N6A 5B7, CANADA
minac@uwo.ca

Andrew Schultz:
Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W. Green Street, Urbana, IL, 61801, USA
acs@math.uiuc.edu

John Swallow:
Department of Mathematics, Davidson College, Box 7046, Davidson, North Carolina 28035-7046, USA
joswallow@davidson.edu