An observation on the cyclicity of the group of the double struck F sign p-rational points of Abelian surfaces

Takuya Yamauchi

doi:10.1007/BF03167542

An observation on the cyclicity of the group of the double struck F sign p-rational points of Abelian surfaces

Takuya Yamauchi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A be a principally polarized Abelian surface defined over Q with End(A) = ℤ and Ã be the reduction at a good prime p. In this paper, we study the density of prime numbers p for which Ã(doubl struck F sign _p) is a cyclic group and establish a conjecture which relates this density.

Original language	English
Pages (from-to)	307-318
Number of pages	12
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/BF03167542
Publication status	Published - 2007 Oct

Keywords

Abelian surface
Cyclicity

Access to Document

10.1007/BF03167542

Cite this

@article{220b1356340c43868519f8b7a9d132af,

title = "An observation on the cyclicity of the group of the double struck F sign p-rational points of Abelian surfaces",

abstract = "Let A be a principally polarized Abelian surface defined over Q with End(A) = ℤ and {\~A} be the reduction at a good prime p. In this paper, we study the density of prime numbers p for which {\~A}(doubl struck F sign p) is a cyclic group and establish a conjecture which relates this density.",

keywords = "Abelian surface, Cyclicity",

author = "Takuya Yamauchi",

year = "2007",

month = oct,

doi = "10.1007/BF03167542",

language = "English",

volume = "24",

pages = "307--318",

journal = "Japan Journal of Industrial and Applied Mathematics",

issn = "0916-7005",

publisher = "Springer Japan",

number = "3",

}

TY - JOUR

T1 - An observation on the cyclicity of the group of the double struck F sign p-rational points of Abelian surfaces

AU - Yamauchi, Takuya

PY - 2007/10

Y1 - 2007/10

N2 - Let A be a principally polarized Abelian surface defined over Q with End(A) = ℤ and Ã be the reduction at a good prime p. In this paper, we study the density of prime numbers p for which Ã(doubl struck F sign p) is a cyclic group and establish a conjecture which relates this density.

AB - Let A be a principally polarized Abelian surface defined over Q with End(A) = ℤ and Ã be the reduction at a good prime p. In this paper, we study the density of prime numbers p for which Ã(doubl struck F sign p) is a cyclic group and establish a conjecture which relates this density.

KW - Abelian surface

KW - Cyclicity

UR - http://www.scopus.com/inward/record.url?scp=38349033279&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349033279&partnerID=8YFLogxK

U2 - 10.1007/BF03167542

DO - 10.1007/BF03167542

M3 - Article

AN - SCOPUS:38349033279

SN - 0916-7005

VL - 24

SP - 307

EP - 318

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

IS - 3

ER -

An observation on the cyclicity of the group of the double struck F sign p-rational points of Abelian surfaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this