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Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$

Gove Griffith Elder — 1995

Annales de l'institut Fourier

For $L / K$ , any totally ramified cyclic extension of degree $p^{2}$ of local fields which are finite extensions of the field of $p$ -adic numbers, we describe the $ℤ_{p} [Gal (L / K)]$ -module structure of each fractional ideal of $L$ explicitly in terms of the $4 p + 1$ indecomposable $ℤ_{p} [Gal (L / K)]$ -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$

Elder Gove Griffith — 1998

Annales de l'institut Fourier

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Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2

Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2

Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$

Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$