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Ganesh Bhandari, Nicole Lemire, Ján Mináč, and John Swallow
Galois module structure of Milnor K-theory in characteristic p
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| Published: |
June 23, 2008
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| Keywords: |
Milnor K-groups modulo p, cyclic extensions, Galois modules |
| Subject: |
19D45, 12F10 |
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Abstract
Let E be a cyclic extension of degree pn of a field F of
characteristic p. Using arithmetic invariants of E/F we
determine km E, the Milnor K-groups Km E modulo p, as
Fp[Gal(E/F)]-modules for all m ∈ N. In particular, we
show that each indecomposable summand of km E has
Fp-dimension a power of p. That all powers pi, i=0, 1,
..., n, occur for suitable examples is shown in a subsequent
paper, Mináč, Schultz and Swallow, 2008, where additionally the main result of this
paper becomes an essential induction step in the determination
of Km E/ps Km E as (Z/psZ)[Gal(E/F)]-modules for all
m, s ∈ N.
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| Acknowledgements
The second author's research was supported in part by NSERC grant R3276A01.
The third author's research was supported in part by NSERC grant R0370A01, and by a Distinguished Research Professorship at the University of Western Ontario.
The fourth author's research was supported in part by NSA grant MDA904-02-1-0061 and by NSF grant DMS-0600122.
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| Author information
Ganesh Bhandari:
Department of Mathematics, Physics and Engineering, Mount Royal College, 4825 Mount Royal Gate SW, Calgary, Alberta T3E 6K6, CANADA
gbhandari@mtroyal.ca
Nicole Lemire:
Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario N6A 5B7, CANADA
nlemire@uwo.ca
Ján Mináč:
Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario N6A 5B7, CANADA
minac@uwo.ca
John Swallow:
Department of Mathematics, Davidson College, Box 7046, Davidson, North Carolina 28035-7046, USA
joswallow@davidson.edu
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