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 50 条

[31] Fine Selmer groups of congruent Galois representations
Lim, Meng Fai
Sujatha, Ramdorai
JOURNAL OF NUMBER THEORY, 2018, 187 : 66 - 91
[32] Galois representations on profinite braid groups on curves
Matsumoto, M
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1996, 474 : 169 - 219
[33] Lie algebras of Galois representations on fundamental groups
Wojtkowiak, Zdzislaw
GALOIS-TEICHMUELLER THEORY AND ARITHMETIC GEOMETRY, 2012, 63 : 601 - 627
[34] Representations over Galois ring of a linear recurring sequence of maximal period over Galois field
Bogonatov, R. V.
DISCRETE MATHEMATICS AND APPLICATIONS, 2007, 17 (01): : 87 - 104
[35] Integral representations of unramified Galois groups and matrix divisors over number fields
Morishita, M
OSAKA JOURNAL OF MATHEMATICS, 1995, 32 (03) : 565 - 576
[36] Galois Representations and the Tame Inverse Galois Problem
Arias-de-Reyna, Sara
Vila, Nuria
WIN - WOMEN IN NUMBERS: RESEARCH DIRECTIONS IN NUMBER THEORY, 2011, 60 : 277 - 288
[37] GROUPS PSL(L+1)P AS GALOIS-GROUPS OVER Q
NUZHIN, YN
DOKLADY AKADEMII NAUK, 1994, 339 (01) : 18 - 20
[38] Automorphic Galois Representations and the Inverse Galois Problem
Arias-de-Reyna, Sara
TRENDS IN NUMBER THEORY, 2015, 649 : 1 - 16
[39] Free pro-p groups as Galois groups over Q(p)(t)
Sonn, J
ISRAEL JOURNAL OF MATHEMATICS, 2000, 119 (1) : 1 - 8
[40] Galois representations of dihedral type over QP
Frederiksen, P
Kiming, I
ACTA ARITHMETICA, 2004, 111 (01) : 43 - 59

← 1 2 3 4 5 →