Colloquium / Seminars
Topic:Cuspidal divisor class groups of the modular curve
Speaker:Prof. Jia--Wei Guo
(National Taiwan University)Date time:Oct. 18, 2022 14:00 – 15:00
Venue:SA223
Abstract:
Abstract. Let $N=p^2M$ with $p$ a prime and $M$ a square free integer, $\mathscr C(N)$ be the subgroup of the Jacobian variety $J_0(N)$ generated by the equivalent classes of cuspidal divisors of degree $0$, and $\mathscr C_{\mathbb Q}(N)$ be the subgroup of $\mathscr C(N)(\mathbb Q)$ generated by $\mathbb Q$-rational cuspidal divisors. In this talk, we will show that the two groups $\mathscr C(N)(\mathbb Q)$ and $\mathscr C_{\mathbb Q}(N)$ are equal by appropriate constructions of modular units. This is a joint work with Yifan Yang, Hwajong Yoo, and Myungjun Yu.Download:Talk_1111018.pdf
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