On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
| dc.creator | Howe, Everett W. | |
| dc.creator | Zhu, Hui June | |
| dc.date | 2000-02-24 | |
| dc.date.accessioned | 2026-07-07T04:34:03Z | |
| dc.date.available | 2026-07-07T04:34:03Z | |
| dc.description | 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, the quantity S(F_q,n) approaches 1 as q approaches infinity over the prime powers. | |
| dc.description | 17 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0002205 | |
| dc.identifier | http://arxiv.org/abs/math/0002205 | |
| dc.identifier | J. Number Theory 92 (2002) 139--163. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58753 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G15 (Primary) 11G10, 14K15 (Secondary) | |
| dc.title | On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field | |
| dc.type | text |