Displaying similar documents to “Galois module structure of generalized jacobians.”

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

Gove Griffith Elder (1995)

Annales de l'institut Fourier

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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.

On Galois structure of the integers in cyclic extensions of local number fields

G. Griffith Elder (2002)

Journal de théorie des nombres de Bordeaux

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Let p be a rational prime, K be a finite extension of the field of p -adic numbers, and let L / K be a totally ramified cyclic extension of degree p n . Restrict the first ramification number of L / K to about half of its possible values, b 1 > 1 / 2 · p e 0 / ( p - 1 ) where e 0 denotes the absolute ramification index of K . Under this loose condition, we explicitly determine the ℤ p [ G ] -module structure of the ring of integers of L , where ℤ p denotes the p -adic integers and G denotes the Galois group Gal ( L / K ) . In the process of determining...