کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9496507 1630683 2005 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Visualizing elements of order two in the Weil-Châtelet group
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Visualizing elements of order two in the Weil-Châtelet group
چکیده انگلیسی
Let E be an elliptic curve over an infinite field K with characteristic ≠2, and σ∈H1(GK,E)[2] a two-torsion element of its Weil-Châtelet group. We prove that σ is always visible in infinitely many abelian surfaces up to isomorphism, in the sense put forward by Cremona and Mazur in their article (J. Exp. Math. 9(1) (2000) 13). Our argument is a variant of Mazur's proof, given in (Asian J. Math. 3(1) (1999) 221), for the analogous statement about three-torsion elements of the Shafarevich-Tate group in the setting where K is a number field. In particular, instead of the universal elliptic curve with full level-three-structure, our proof makes use of the universal elliptic curve with full level-two-structure and an invariant differential.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 110, Issue 2, February 2005, Pages 387-395
نویسندگان
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