论文标题
缺陷扩展和驯服场的表征
Defect extensions and a characterization of tame fields
论文作者
论文摘要
我们研究了两个重要的有价值领域的两个重要类别之间的关系：驯服场和无缺陷领域。我们表明，在具有相等特征或等级的混合特征的一个有价值字段的有价值字段的情况下，驯服场正是所有代数扩展的有价值字段。总的来说，驯服场形成了一个有价值字段的适当子类，所有代数扩展都是无缺陷场。我们介绍了更广泛的大致温和的字段，并表明当给定有价值字段的每个代数扩展是毫无障碍的，并且仅当其henselization大致驯服时。证明上述结果我们还介绍了阳性和混合特征的Galois缺陷扩展的结构。
We study the relation between two important classes of valued fields: tame fields and defectless fields. We show that in the case of valued fields of equal characteristic or rank one valued fields of mixed characteristic, tame fields are exactly the valued fields for which all algebraic extensions are defectless fields. In general tame fields form a proper subclass of valued fields for which all algebraic extensions are defectless fields. We introduce a wider class of roughly tame fields and show that every algebraic extension of a given valued field is defectless if and only if its henselization is roughly tame. Proving the above results we also present constructions of Galois defect extensions in positive as well as mixed characteristic.
