Galois Representations and Galois Groups Over Q

被引：2

作者：

Arias-de-Reyna, Sara

Armana, Cecile ^{[1
]}

Karemaker, Valentijn ^{[2
]}

Rebolledo, Marusia ^{[3
]}

Thomas, Lara ^{[4
]}

Vila, Nuria ^{[5
]}

机构：

[1] Univ Franche Comtee, Math Lab, Besancon, France

[2] Univ Utrecht, Math Inst, Utrecht, Netherlands

[3] Univ Blaise Pascal, Math Lab, Aubiere, France

[4] ENS, Pure & Appl Math Unit, Lyon, France

[5] Univ Barcelona, Dept Algebra & Geometry, Barcelona, Spain

来源：

WOMEN IN NUMBERS EUROPE: RESEARCH DIRECTIONS IN NUMBER THEORY | 2015年 / 2卷

关键词：

GEOMETRIC FAMILIES; MODULAR-FORMS; IMAGES; GENUS-2; POINTS; CURVES; ORDER;

D O I：

10.1007/978-3-319-17987-2_8

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve, let J(C) be the associated Jacobian variety, and let (rho) over bar (l) : G(Q) -> GSp(J(C)[l]) be the Galois representation attached to the l-torsion of J(C). Assume that there exists a prime p such that J(C) has semistable reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes l (if they exist) such that (rho) over bar (l) is surjective. In particular we realize GSp(6)(F-l) as a Galois group over Q for all primes l is an element of [11, 500,000].

引用

页码：191 / 205

页数：15

共 33 条

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[Anonymous], 2013, PREPRINT

[2]

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[3]

Arias-de-Reyna S., 2014, DEMONSTRATIO MATH

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