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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Towers of surfaces dominated by products of curves and elliptic curves of large rank over function fields
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