On the closed subfields of \(C_p\)
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Publication:1379639
DOI10.1006/jnth.1997.2198zbMath0901.11035OpenAlexW2005515483WikidataQ105439581 ScholiaQ105439581MaRDI QIDQ1379639
Alexandru Zaharescu, Nicolae Popescu, Victor Alexandru
Publication date: 31 August 1998
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1997.2198
topological closure\(p\)-adic fieldsalgebraic extensionsclosed subfields of \(C_p\)generic transcendental elements
Related Items (27)
AN ALGEBRAIC-METRIC EQUIVALENCE RELATION OVER p-ADIC FIELDS ⋮ On the closed subfields of \(\overset\simeq {\mathbb{Q}}_p\) ⋮ Integral representations and the behavior of Krasner analytic functions around singular points ⋮ Derivations and generating degrees in the ring of arithmetical functions ⋮ Continuous automorphisms of transcendental closed subfields of \(\mathbb {C}_p\) ⋮ Relative spectral norm on algebraic numbers ⋮ Galois equivariant functions on Galois orbits in large \(p\)-adic fields ⋮ Trace series on \(\tilde {\mathbb Q}_k\) ⋮ Representation results for equivariant rigid analytic functions ⋮ The behaviour of rigid analytic functions around orbits of elements of \(\mathbb C_p\) ⋮ On the zeros of Krasner analytic functions ⋮ Absorbent property, Krasner type lemmas and spectral norms for a class of valued fields ⋮ Unnamed Item ⋮ Analytic normal basis theorem ⋮ On Limits of Sequences of Algebraic Elements over a Complete Field ⋮ The \(p\)-adic measure on the orbit of an element of \(\mathbb{C}_p\) ⋮ Trace on \(\mathbb{C}_p\) ⋮ On the Iwasawa algebra associated to a normal element of \(\mathbb C_p\) ⋮ On p-adic analytic continuation with applications to generating elements ⋮ A representation theorem for a class of rigid analytic functions ⋮ On the existence of trace for elements of \(\mathbb{C}_p\) ⋮ Generating sets of Galois equivariant Krasner analytic functions ⋮ ON SATURATED DISTINGUISHED CHAINS OVER A LOCAL FIELD III: The Case of p-Extensions with Two Proper Higher Ramification Groups ⋮ \(v\)-adic maximal extensions, spectral norms and absolute Galois groups ⋮ A notion analogous to the discriminant for transcendental elements in certain extensions of local fields ⋮ On the zeros and singularities of p−adic trace functions ⋮ On the norm of Krasner analytic functions with applications to transcendence results
Cites Work
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- A theorem of characterization of residual transcendental extensions of a valuation
- Minimal pairs of definition of a residual transcendental extension of a valuation
- All valuations on K(X)
- On the residual transcendental extensions of a valuation. Key polynomials and augmented valuation
- Completions of r.a.t.-valued fields of rational functions
- Some elementary remarks about \(n\)-local fields
- On the structure of the irreducible polynomials over local fields
- Nondiscrete local ramified class field theory
- Completion of r.t. extensions of local fields. I
- Zeros of polynomials over local fields. The Galois action
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