Galois representations and Galois groups over Q
Association for Women in Mathematics Series(2015)
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].
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关键词
Modular Form, Characteristic Polynomial, Galois Group, Abelian Variety, Galois Representation
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