Weil Numbers Generated by Other Weil Numbers and Torsion Fields of Abelian Varieties

نویسنده

  • E. KOWALSKI
چکیده

Using properties of the Frobenius eigenvalues, we show that, in a precise sense, “most” isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized, up to isogeny, by the sequence of their division fields, and a similar result for “most” isogeny classes. Some global cases are also treated.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Complete characterization of the Mordell-Weil group of some families of elliptic curves

 The Mordell-Weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎In our previous paper, H‎. ‎Daghigh‎, ‎and S‎. ‎Didari‎, On the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎Bull‎. ‎Iranian Math‎. ‎Soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using Selmer groups‎, ‎we have shown that for a prime $p...

متن کامل

Abelian varieties over finite fields

A. Weil proved that the geometric Frobenius π = Fa of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer s...

متن کامل

A Mordell-weil Theorem for Abelian Varieties over Fields Generated by Torsion Points

Let A be an abelian variety over a number field, Tl the ladic Tate module, and Gl the image of the Galois action on Tl. Then Hi(Gl, Tl) is a finite l-group which vanishes for l ≫ 0. We apply this bound for i = 1 and i = 2 to show that ifK denotes the field generated by all torsion points of A, then A(K) is the direct sum of its torsion group and a free abelian group.

متن کامل

18.782 Arithmetic Geometry Lecture Note 25

In the last lecture we proved that the torsion subgroup of the rational points on an elliptic curve E/Q is finite. In this lecture we will prove a special case of Mordell’s theorem, which states that E(Q) is finitely generated. By the structure theorem for finitely generated abelian groups, this implies E(Q) ' Z ⊕ T, where Zr is a free abelian group of rank r, and T is the (necessarily finite) ...

متن کامل

Principally Polarized Ordinary Abelian Varieties over Finite Fields

Deligne has shown that there is an equivalence from the category of ordinary abelian varieties over a finite field A: to a category of Z-modules with additional structure. We translate several geometric notions, including that of a polarization, into Deligne's category of Z-modules. We use Deligne's equivalence to characterize the finite group schemes over k that occur as kernels of polarizatio...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005