Rational Torsion of Generalised Modular Jacobians

Abstract: We consider the generalized Jacobian $J_0(N)_m$ of the modular curve $X_0(N)$ of level $N$, with respect to the modulus $m$ consisting of all cusps on the modular curve. When $N=p^(r)q^(s)$, for $p$ and $q$ odd prime numbers, we determine the group structure of the rational torsion of the Jacobian $J_0(N)_m$ up to 2-primary, $p$-primary and $q$-primary torsion. Our results extend known results for squarefree levels and for prime power levels. Our proofs use their techniques, as well as results concerning the study of the rational points on the modular Jacobian and of the rational divisor class group of $X_0(N)$.

number theory

Audience: researchers in the discipline

Comments: Register here: umanitoba.zoom.us/meeting/register/u5csf-CtqzstEtfTaoLl6L8gnaVIJnGVB49w

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POINT: New Developments in Number Theory

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