Rational torsion points on Jacobians of Shimura curves

2015/02/25 by Yoo, Hwajong
#11G10 #11G18 #14G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1502.07370

Abstract

Let p and q be distinct primes. Consider the Shimura curve X associated to the indefinite quaternion algebra of discriminant pq over ℚ. Let J be the Jacobian variety of X, which is an abelian variety over ℚ. For an odd prime ℓ, we provide sufficient conditions for the non-existence of rational points of order ℓ on J. As an application, we find some non-trivial subgroups of the kernel of an isogeny from the new quotient of J₀(pq) to J.

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