Algebraic Geometry & Number Theory Seminar

DATE2020-03-03 15:30-16:30


SPEAKER楊一帆 教授(台灣大學數學系

TITLEModular Units and Cuspidal Divisor Classes on X_0(n^2M) with n|24 and M squarefree

ABSTRACT 本演講學者因事取消
For a positive integer N, let C(N) be the subgroup of J_0(N) generated by all cuspidal divisors of degree 0 and C(N)(\mathbb Q) be its rational subgroup. Let also C_{\mathbb Q}(N) be the subgroup of C(N)(\mathbb Q) generated by \mathbb Q-rational cuspidal divisors. We prove that when N=n^2M for some integer n dividing 24 and some squarefree integer M, the two groups C(N)(\mathbb Q) and C_{\mathbb Q}(N) are equal. To achieve this, we determine all the modular units on X_0(N) for such level N. This is a joint work with Liuquan Wang.