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- W1974013335 abstract "Let K be a finite extension of Q p , and suppose that K / Q p is ramified and that the residue field of K has cardinality at least 3. Let K (2) be the second division field of K with respect to a Lubin–Tate formal group, and let Γ =Gal( K (2) / K ). We determine the associated order in KΓ of the valuation ring O (2) of K (2) , and show that O (2) is not free over this order. The integral Galois module structure of certain intermediate fields E of K (2) / K is also considered. In particular, if p ≠2 and K has residue field of cardinality p or p 2 , we show that the valuation ring of E is free over its associated order if and only if E / K is either tamely ramified or a p -extension. We also prove that the valuation ring of any weakly ramified abelian extension of K is free over its associated order." @default.
- W1974013335 created "2016-06-24" @default.
- W1974013335 creator A5067334578 @default.
- W1974013335 date "1999-08-01" @default.
- W1974013335 modified "2023-10-16" @default.
- W1974013335 title "Integral Galois Module Structure of Some Lubin–Tate Extensions" @default.
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- W1974013335 doi "https://doi.org/10.1006/jnth.1999.2385" @default.
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