## 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.

### MSC:

 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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### References:

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