On the local Artin conductor \(\mathfrak f_{\text{Artin}}(\chi)\) of a character \(\chi\) of \(\text{Gal}(E/K)\). II: Main results for the metabelian case (Q1422299)
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scientific article; zbMATH DE number 2040287
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the local Artin conductor \(\mathfrak f_{\text{Artin}}(\chi)\) of a character \(\chi\) of \(\text{Gal}(E/K)\). II: Main results for the metabelian case |
scientific article; zbMATH DE number 2040287 |
Statements
On the local Artin conductor \(\mathfrak f_{\text{Artin}}(\chi)\) of a character \(\chi\) of \(\text{Gal}(E/K)\). II: Main results for the metabelian case (English)
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11 February 2004
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Let \(K\) be a local field and \(E/K\) a metabelian Galois extension with Galois group \(G\). Furthermore let \(A_G: G\to\text{GL}(V)\) be the Artin representation with character \(a_G\). The author computes the Artin conductor of an irreducible representation of \(G\). He uses this result to give an answer in the metabelian case to the old question of constructing \(A_G\) if \(a_G\) is given. Part I, cf. Turk. J. Math. 23, No. 4, 519--530 (1999; Zbl 1006.11067).
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