Wild Ramification in the Imperfect Residue Field Case

Hyodo, Osamu

doi:10.2969/aspm/01210287

Cited by 32 publications

(19 citation statements)

References 2 publications

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“…Then, Hyodo [5, implies L = M(y 1/p ) with y = w where w is a unit of M and is a prime element of M. Hence, L/K t would be a non-abelian extension. This is a contradiction.…”

Section: Some Results On a Trace Mapmentioning

confidence: 94%

On the norm maps of formal groups for Zp-extensions

Kuriya

2005

Journal of Number Theory

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“…Then, Hyodo [5, implies L = M(y 1/p ) with y = w where w is a unit of M and is a prime element of M. Hence, L/K t would be a non-abelian extension. This is a contradiction.…”

Section: Some Results On a Trace Mapmentioning

confidence: 94%

On the norm maps of formal groups for Zp-extensions

Kuriya

2005

Journal of Number Theory

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“…Known results on the non-classical case include Kato's class field theory for "ndimensional complete discrete valuation fields," see [6] and [4]. In Zariski-Samuel [12, Vol.…”

Section: Introductionmentioning

confidence: 99%

The different and differentials of local fields with imperfect residue fields

Smit

1997

Proceedings of the Edinburgh Mathematical Society

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Let K be a complete field with respect to a discrete valuation and let L be a finite Galois extension of K. If the residue field extension is separable then the different of L/K can be expressed in terms of the ramification groups by a well-known formula of Hilbert. We will identify the necessary correction term in the general case, and we give inequalities for ramification groups of subextensions L'/K in terms of those of L/K. A question of Krasner in this context is settled with a counterexample. These ramification phenomena can be related to the structure of the module of differentials of the extension of valuation rings. For the case that, where p is the residue characteristic, this module is shown to determine the correction term in Hilbert's formula.1991 Mathematics subject classification: 11S15, 13N05.

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“…where both L and M are finite extensions of K. [Hy,). This is important for discussing examples in the subsequent sections.…”

Section: 2-23])mentioning

confidence: 99%

“…where ( [Hy,]. If L/K is a Galois extension with the Galois group G, for any g ∈ G one defines the Artin and Swan ramification numbers by the formulas…”

Section: For Any Integral Scheme S K(s) Is the Field Of Rational Funmentioning

confidence: 99%