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In mathematics, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by as an expression appearing in the functional equation of an Artin L-function. ==Local Artin conductors== Suppose that ''L'' is a finite Galois extension of the local field ''K'', with Galois group ''G''. If χ is a character of ''G'', then the Artin conductor of χ is the number : where ''G''''i'' is the ''i''-th ramification group (in lower numbering), of order ''g''''i'', and χ(''G''''i'') is the average value of χ on ''G''''i''.〔Serre (1967) p.158〕 By a result of Artin, the local conductor is an integer.〔Serre (1967) p.159〕 If χ is unramified, then its Artin conductor is zero. If ''L'' is unramified over ''K'', then the Artin conductors of all χ are zero. The ''wild invariant''〔 or ''Swan conductor''〔Snaith (1994) p.249〕 of the character is : in other words, the sum of the higher order terms with ''i'' > 0. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Artin conductor」の詳細全文を読む スポンサード リンク
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