A monogenic Hasse-Arf theorem. (English) Zbl 1077.13011

Let \(B/A\) be a finite extension of Henselian discrete valuation rings and assume that the corresponding extension of fraction fields is Galois with group \(G\). For any finite dimensional complex representation of \(G\) the naive Artin conductor is defined and it is always a nonnegative rational number. When \(B/A\) is residually separable, the Hasse-Arf theorem asserts that the conductor is an integer. When instead of separability one requires that \(B\) is generated as an \(A\)-algebra by one element, the extension \(B/A\) is said to be monogenic. The author proves that for monogenic extensions the conductor is also an integer by reducing the proof to the classical context of the Hasse-Arf theorem.


13F30 Valuation rings
13B02 Extension theory of commutative rings
11S15 Ramification and extension theory
13J15 Henselian rings
12F15 Inseparable field extensions
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