Quaternion Algebras over Curves of Genus One Without Rational Points

• 来源期刊: 代数集刊（英文版）
• 关键词: quaternion algebras curves of genus one Azumaya algebras Hasse principle unramified quaternion algebras
• 年，卷（期）: 2005,（1）
• 页码范围: 67-92
• 页数: 26页
• 语种: 英文

摘要

Quaternion algebras over curves of genus one without rational points over perfect fields of characteristic not two are classified. As a consequence, all quaternion algebras over the function field of such a curve, which are unramified everywhere, are classified.