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Birch's lemma over global function fields


Authors: Yi Ouyang and Shenxing Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 577-584
MSC (2010): Primary 11G05; Secondary 11D25, 11G40
DOI: https://doi.org/10.1090/proc/13265
Published electronically: October 24, 2016
MathSciNet review: 3577862
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Abstract: We obtain a function field version of Birch's Lemma, which reveals non-torsion points in quadratic twists of an elliptic curve over a global function field, where the quadratic twists have many prime factors. The proof uses Brown's Euler system of Heegner points over function fields and a result of Vigni on the ring class eigenspaces of Mordell-Weil groups in positive characteristic.


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Additional Information

Yi Ouyang
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: yiouyang@ustc.edu.cn

Shenxing Zhang
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: zsxqq@mail.ustc.edu.cn

DOI: https://doi.org/10.1090/proc/13265
Received by editor(s): December 16, 2015
Received by editor(s) in revised form: April 21, 2016, and April 30, 2016
Published electronically: October 24, 2016
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2016 American Mathematical Society