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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
Let E be an elliptic curve over an infinite field K with characteristic â 2, and ÏâH1(GK,E)[2] a two-torsion element of its Weil-Châtelet group. We prove that Ï 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
Journal: Journal of Number Theory - Volume 110, Issue 2, February 2005, Pages 387-395
نویسندگان
Tomas Antonius Klenke,