Galois module structure of Milnor K-theory in characteristic p
Number Theory
2008-06-26 v5 K-Theory and Homology
Representation Theory
Abstract
Let E be a cyclic extension of degree p^n of a field F of characteristic p. Using arithmetic invariants of E/F we determine k_mE, the Milnor K-groups K_mE modulo p, as Fp[Gal(E/F)]-modules for all m in N. In particular, we show that each indecomposable summand of k_mE has Fp-dimension a power of p. That all powers p^i, i=0,1,...,n, occur for suitable examples is shown in a subsequent paper [MSS2], where additionally the main result of this paper becomes an essential induction step in the determination of K_mE/p^sK_mE as (Z/p^sZ)[Gal(E/F)]-modules for all m, s in N.
Cite
@article{arxiv.math/0405503,
title = {Galois module structure of Milnor K-theory in characteristic p},
author = {Ganesh Bhandari and Nicole Lemire and Jan Minac and John Swallow},
journal= {arXiv preprint arXiv:math/0405503},
year = {2008}
}
Comments
v5 (10 pages); revised introduction and shortened paper; incorporated and acknowledged suggestions by readers of earlier versions