Geodesic
Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
Documenta mathematica, Tome 21 (2016), pp. 1669-1690.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We consider the generalized Jacobian $\widetilde{J}_{0}(N)$ of a modular curve $X_{0}(N)$ with respect to a reduced divisor given by the sum of all cusps on it. When $N$ is a power of a prime $\geq 5$, we exhibit that the group of rational torsion points $\widetilde{J}_{0}(N)(\mathbb {Q})_{\text{Tor}}$ tends to be much smaller than the classical Jacobian.
Classification : 14H40, 11G16
Keywords: modular curves, cuspidal divisor classes, generalized Jacobian varieties, torsion points 
@article{DOCMA_2016__21__a1,
     author = {Yamazaki, Takao and Yang, Yifan},
     title = {Rational torsion on the generalized {Jacobian} of a modular curve with cuspidal modulus},
     journal = {Documenta mathematica},
     pages = {1669--1690},
     publisher = {mathdoc},
     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a1/}
}
TY  - JOUR
AU  - Yamazaki, Takao
AU  - Yang, Yifan
TI  - Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
JO  - Documenta mathematica
PY  - 2016
SP  - 1669
EP  - 1690
VL  - 21
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a1/
LA  - en
ID  - DOCMA_2016__21__a1
ER  - 
%0 Journal Article
%A Yamazaki, Takao
%A Yang, Yifan
%T Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
%J Documenta mathematica
%D 2016
%P 1669-1690
%V 21
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a1/
%G en
%F DOCMA_2016__21__a1
Yamazaki, Takao; Yang, Yifan. Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus. Documenta mathematica, Tome 21 (2016), pp. 1669-1690. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a1/