1. CMB 2011 (vol 55 pp. 233)
|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
2. CMB 2005 (vol 48 pp. 428)
|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)
|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