On the Existence of Absolutely Simple Abelian Varieties of a Given Dimension over an Arbitrary Field |
| |
Authors: | Everett W HoweHui June Zhu |
| |
Institution: | a Center for Communications Research, 4320 Westerra Court, San Diego, California, 92121-1967, f1E-mail: however@alumni.caltech.eduf1, http://alumni.caltech.edu/∼however/b Department of Mathematics, University of California, Berkeley, California, 94720-3880, f2E-mail: zhu@alum.calberkeley.orgf2 |
| |
Abstract: | We prove that for every field k and every positive integer n there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite fields: For every finite field k and positive integer n, we let S(k, n) denote the fraction of the isogeny classes of n-dimensional abelian varieties over k that consist of absolutely simple ordinary abelian varieties. Then for every n we have S(Fq, n)→1 as q→∞ over the prime powers. |
| |
Keywords: | Abelian variety finite field absolute simplicity |
本文献已被 ScienceDirect 等数据库收录! |
|