کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771602 | 1630358 | 2017 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the order of CM abelian varieties over finite prime fields
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let A be a principally polarized CM abelian variety of dimension d defined over a number field F containing the CM-field K. Let â be a prime number unramified in K/Q. The Galois group Gâ of the â-division field of A lies in a maximal torus of the general symplectic group of dimension 2d over Fâ. Relying on a method of Weng, we explicitly write down this maximal torus as a matrix group. We restrict ourselves to the case that Gâ equals the maximal torus. If p is a prime ideal in F with p|p, let Ap be the reduction of A modulo p. By counting matrices with eigenvalue 1 in Gâ we obtain a formula for the density of primes p such that the â-rank of Ap(Fp) is at least 1. Thereby we generalize results of Koblitz and Weng who computed this density for d=1 and 2. Both authors gave conjectural formulae for the number of primes p with norm less than n such that Ap(Fp) has prime order. We describe the involved heuristics, generalize these conjectures to arbitrary d and provide examples with d=3.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 45, May 2017, Pages 386-405
Journal: Finite Fields and Their Applications - Volume 45, May 2017, Pages 386-405
نویسندگان
Ute Spreckels,