Rational torsion points on Jacobians of modular curves

• Autorzy: Hwajong Yoo
• Języki publikacji: EN

Abstrakty

EN

Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let 𝓣(3p) and 𝓒(3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of 𝓣(3p) and 𝓒(3p) coincide unless p ≡ 1 (mod 9) and $3^{(p-1)/3} ≡ 1 (mod p)$.

Kategorie tematyczne

• 11G10: Abelian varieties of dimension > 1
• 14G05: Rational points
• 11G18: Arithmetic aspects of modular and Shimura varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 4
• Strony: 299-304

Daty

wydano

2016

Twórcy

autor

Hwajong Yoo

• Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea

Identyfikatory

DOI

10.4064/aa8140-12-2015