کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593790 1630670 2014 45 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Examples of non-simple abelian surfaces over the rationals with non-square order Tate–Shafarevich group
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Examples of non-simple abelian surfaces over the rationals with non-square order Tate–Shafarevich group
چکیده انگلیسی

Let A be an abelian surface over a fixed number field. If A is principally polarised, then it is known that the order of the Tate–Shafarevich group of A   must, if finite, be a square or twice a square. For each k∈{1,2,3,5,6,7,10,13}k∈{1,2,3,5,6,7,10,13} we construct a non-simple non-principally polarised abelian surface B/QB/Q having Tate–Shafarevich group of order k times a square. To obtain this result, we explore the invariance under isogeny of the Birch and Swinnerton–Dyer conjecture.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 144, November 2014, Pages 25–69
نویسندگان
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