کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772703 1630640 2017 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the local-global divisibility of torsion points on elliptic curves and GL2-type varieties
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the local-global divisibility of torsion points on elliptic curves and GL2-type varieties
چکیده انگلیسی

Let p be a prime number and let k be a number field. Let E be an elliptic curve defined over k. We prove that if p is odd, then the local-global divisibility by any power of p holds for the torsion points of E. We also show with an example that the hypothesis over p is necessary.We get a weak generalization of the result on elliptic curves to the larger family of GL2-type varieties over k. In the special case of the abelian surfaces A/k with quaternionic multiplication over k we obtain that for all prime numbers p, except a finite number depending only on the isomorphism class of the ring Endk(A), the local-global divisibility by any power of p holds for the torsion points of A.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 174, May 2017, Pages 202-220
نویسندگان
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