One-dimensional elementary abelian extensions have Galois scaffolding

Details One-dimensional elementary abelian extensions have Galois scaffolding One-dimensional elementary abelian extensions have Galois scaffolding

2005-11-07

arxiv.org/abs/math/0511174v2

Mathematics

Number Theory

13 pages. This is a revision of "One-dimensional elementary-abelian extensions of local fields," which is being split into two

Scientific paper

We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local function fields of characteristic $p$, called {\em one-dimensional}, that, in a particular sense, are as simple as cyclic degree $p$ extensions, and prove the statement in the title above.

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