کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4594985 | 1335792 | 2008 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Towers of surfaces dominated by products of curves and elliptic curves of large rank over function fields
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
With the goal of producing elliptic curves and higher-dimensional abelian varieties of large rank over function fields, we provide a geometric construction of towers of surfaces dominated by products of curves; in the case where the surface is defined over a finite field our construction yields families of smooth, projective curves whose Jacobians satisfy the conjecture of Birch and Swinnerton-Dyer. As an immediate application of our work we employ known results on analytic ranks of abelian varieties defined in towers of function field extensions, producing a one-parameter family of elliptic curves over Fq(t1/d) whose members obtain arbitrarily large rank as d→∞.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 12, December 2008, Pages 3013-3030
Journal: Journal of Number Theory - Volume 128, Issue 12, December 2008, Pages 3013-3030