Tractability of algebraic function fields in one variable of genus one over global fields

JOURNAL OF ALGEBRA

卷:317

Article

Han, Ilseop¹ 

[1] Calif State Univ San Bernardino, Dept Math, San Bernardino, CA 92407 USA

关键词: tractability;    function fields;    genus one;    quaternion algebras;    global fields;   

DOI  :  10.1016/j.jalgebra.2007.04.012

来源: Elsevier

【 摘 要 】

A field k of characteristic unequal to 2 is called tractable if for every nonzero a(i), b(i) epsilon k, i = 1, 2, 3, whenever the quaternion algebra (a(i), b(j)/k) is split for all i not equal j and (a(1), b(1)/k) congruent to (a(2), b(2)/k) congruent to (a(3), b(3)/k), then (a(i), b(i)/k) is split. In the present paper, we study tractability of algebraic function fields in one variable over global fields and give specific examples of tractable function fields and intractable function fields of genus one over Q, the rationals. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free