arXiv 1106.42552011-06math.NT

Tate-Shafarevich群中的Weil-Châtelet可除元I：Q上椭圆曲线的Bashmakov问题

Weil-Châtelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

Mirela Çiperiani, Jakob Stix

备注：: 22 pages, changed title, the origional manuscript arXiv:1106.4255v1 was split in two parts according to Div-questions (part I) and div-questions (part II: Weil-Châtelet divisible elements in Tate-Shafarevich groups II: On a question of Cassels)
发表信息：: Compositio Math. 149 (2013) 729-753
DOI：: 10.1112/S0010437X12000747

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

摘要：

对数域k上的阿贝尔簇A，讨论了H ^1（k，A）的极大可除子群及其与子群Sha（A/k）的交.对于Q上的椭圆曲线，所得结果是最完备的.

英文摘要：

For an abelian variety A over a number field k we discuss the maximal divisibile subgroup of H^1(k,A) and its intersection with the subgroup Sha(A/k). The results are most complete for elliptic curves over Q.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。