Galois Representations and Galois Groups Over ℚ
Galois Representations and Galois Groups Over ℚ
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 and let J(C) be the associated Jacobian variety. 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 the Galois representation attached to the l-torsion of J(C) is surjective onto the group GSp(2n, l). In particular we realize GSp(6, l) as a Galois group over Q for all primes l in [11, 500000].
Minor changes. 13 pages. This paper contains results of the collaboration started at the conference Women in numbers - Europe, (October 2013), by the working group "Galois representations and Galois groups over Q"
- French National Centre for Scientific Research France
- Theological University Netherlands
- Utrecht University Netherlands
- University of Seville Spain
- UNIVERSITE MARIE ET LOUIS PASTEUR France
Mathematics(all), inverse Galois problem over Q, Characteristic Polynomial, 12F12, 11F80, 11G30, 11R32, Mathematics - Number Theory, General Mathematics, Galois Group, 500, Modular Form, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 510, Gender Studies, Galois Representation, Taverne, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Abelian Variety, : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Number Theory (math.NT), Galois representation, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Mathematics(all), inverse Galois problem over Q, Characteristic Polynomial, 12F12, 11F80, 11G30, 11R32, Mathematics - Number Theory, General Mathematics, Galois Group, 500, Modular Form, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 510, Gender Studies, Galois Representation, Taverne, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Abelian Variety, : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Number Theory (math.NT), Galois representation, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
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