Art

J-GLOBAL ID：201502202753113039   Reference number：15A1240644

Computing the Mordell-Weil Groups of Hyperelliptic Jacobians

超楕円Jacobi多様体のMordell-Weil群の計算

Author (1)： UCHIDA YUKIHIRO (首都大学東京 大学院理工学研究科)
Material： 日本応用数理学会論文誌  (Transactions of the Japan Society for Industrial and Applied Mathematics)
Volume： 25  Issue： 3  Page： 229-253  Publication year： Sep. 25, 2015 
JST Material Number： L1010A  ISSN： 0917-2246  Document type： Article
Article type： 文献レビュー  Country of issue： Japan (JPN)  Language： JAPANESE (JA)

Thesaurus term： *manifold(mathematics) ,  *curve ,  *group theory ,  algorithm ,  Abelian group ,  *formula manipulation
Semi thesaurus term： Jacobi多様体 ,  hyperelliptic curve ,  Mordell-Weil群 ,  characteristic ,  algebraic curve

JST classification (3)： Mathematical physics  (BA03000W) ,  Numerical computation  (JE02000J) ,  Symbol manipulation  (JE03000Q)

Reference (65)：

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• Bruin, N., Success and challenges in determining the rational points on curves, ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Howe, E. W. and Kedlaya, K. S., eds., The Open Book Series, 1, Mathematical Sciences Publishers, Berkeley, 2013, 187-212.
• Bruin, N., Flynn, E. V. and Testa, D., Descent via (3, 3)-isogeny on Jacobians of genus 2 curves, Acta Arith., 165 (2014), 201-223.
• Bruin, N., Poonen, B. and Stoll, M., Generalized explicit descent and its application to curves of genus 3, preprint, (2013), arXiv : 1205.4456v2 [math. NT].

Terms in the title (3)： 超楕円 ,  多様体 ,  計算