ENUMERATION OF ISOMORPHISM CLASSES OF EXTENSIONS OF p-ADIC FIELDS
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چکیده
Let Ω be an algebraic closure of Qp and let F be a finite extension of Qp contained in Ω. Given positive integers f and e, the number of extensions K/F contained in Ω with residue degree f and ramification index e was computed by Krasner. This paper is concerned with the number I(F, f, e) of F -isomorphism classes of such extensions. We determine I(F, f, e) completely when p2 ∤ e and get partial results when p2 ‖ e. When s is large, I(Qp, f, e) is equal to the number of isomorphism classes of finite commutative chain rings with residue field Fpf , ramification index e, and length s.
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تاریخ انتشار 2008