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1. CMB 2011 (vol 55 pp. 233)
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On Algebraically Maximal Valued Fields and Defectless Extensions Let $v$ be a Henselian Krull valuation of a field $K$. In this paper,
the authors give some necessary and sufficient conditions for a
finite simple extension of $(K,v)$ to be defectless. Various
characterizations of algebraically maximal valued fields are also
given which lead to a new proof of a result proved by Yu. L. Ershov.
Keywords:valued fields, non-Archimedean valued fields Categories:12J10, 12J25 |
2. CMB 2005 (vol 48 pp. 428)
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Reduction of Elliptic Curves in Equal Characteristic~3 (and~2) and fibre type for elliptic curves
over discrete valued fields of equal characteristic~3.
Along the same lines, partial results are obtained
in equal characteristic~2.
Categories:14H52, 14K15, 11G07, 11G05, 12J10 |
3. CMB 2002 (vol 45 pp. 71)
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Images of Additive Polynomials in $\FF_q ((t))$ Have the Optimal Approximation Property We show that the set of values of an additive polynomial in several
variables with arguments in a formal Laurent series field over a
finite field has the optimal approximation property: every element in
the field has a (not necessarily unique) closest approximation in this
set of values. The approximation is with respect to the canonical
valuation on the field. This property is elementary in the language
of valued rings.
Categories:12J10, 12L12, 03C60 |