Results 1 to 10 of about 437 (84)
Ramification theory for Artin–Schreier extensions of valuation rings
Journal of Algebra, 2016 The goal of this paper is to generalize and refine the classical ramification theory of complete discrete valuation rings to more general valuation rings, in the case of Artin-Schreier extensions. We define refined versions of invariants of ramification in the classical ramification theory and compare them. Furthermore, we can treat the defect case.
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Ramification theory for degree p extensions of arbitrary valuation rings in mixed characteristic (0, p ) [PDF]
Journal of Algebra, 2018 We previously obtained a generalization and refinement of results about the ramification theory of Artin-Schreier extensions of discretely valued fields in characteristic $p$ with perfect residue fields to the case of fields with more general valuations and residue fields. As seen in VT16, the "defect" case gives rise to many interesting complications.
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Pure and Applied Mathematics JournalThis article traces the genesis of a theorem that gives for the first time examples of the Galois group <I>G<SUB>S</SUB></I> of the maximal <i>p</i>-extension of ℚ, unramified outside a finite set of primes not containing an odd <i>p</i ...
John Labute
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Communications in Advanced Mathematical Sciences, 2019 The theory of $p$-ramification, regarding the Galois group of the maximal pro-$p$-extension of a number field $K$, unramified outside $p$ and $\infty$, is well known including numerical experiments with PARI/GP programs.
Georges Gras
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Ramification Theory for Extensions of Degree p [PDF]
Nagoya Mathematical Journal, 1971 The notions of tame and wild ramification lead us to make the following definition.Definition. The quotient field extension of an extension of discrete rank one valuation rings is said to be fiercely ramified if the residue class field extension has a nontrivial inseparable part.
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Ramification Theory for Extensions of Degree p. II [PDF]
Nagoya Mathematical Journal, 1972 Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction ...
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Iwasawa Theory for Extensions with Restricted $p$-Ramification
Tokyo Journal of Mathematics, 2003 For a number field \(K\) and a prime number \(p,\) let \(T\) be a subset of the set \(S\) of \(p\)-primes of \(K\) and \(\mathcal Y_T\) be the \(T\)-ramified (i.e. unramified outside \(T)\) Iwasawa module attached to the cyclotomic \(\mathbb Z_p\)-extension of \(K\). This paper deals mainly with the \(\wedge\)-rank of \(\mathcal Y_T\).
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Journal of Number Theory, 2003 AbstractIn the original Section 3.3, the main result is Theorem 29. In the proof of this Theorem, we use the fact that the cyclotomic extension k∞ is not contained in ∏p∈SℓkSp̄ (except for the trivial case N=Q). In fact, there is one other exception: the imaginary quadratic field. Moreover, there were some imprecisions in Proposition 28.
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, 2000 Ramification theory of monogenic extensions of complete discrete valuation fields is presented. Relations to Kato's conductor are discussed.
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Extensions of discrete valuations & their ramification theory
, 2020 We study how a discrete valuation v on a eld K can be extended to a valuationof a finite separable extension L of K. The ramification theory of extensions of discretevaluations to a finite separable extension is very well established whenever theresidue class field extension is separable. This is the so called classical ramificationtheory.
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