On Eisenstein ideals and the cuspidal group of J₀(N)

2015/02/05 by Hwajong Yoo, Yoo, Hwajong · 1 citation
Mathematics · #11G18 #14G35 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G18 #msc:14G35

paper · pdf · doi:10.48550/arxiv.1502.01571

comments are welcome

arxiv created 2015/10/25 · arxiv updated 2015/10/27

Abstract

Let C_N be the cuspidal subgroup of the Jacobian J₀(N) for a square-free integer N>6. For any Eisenstein maximal ideal \mathfrakm of the Hecke ring of level N, we show that C_N[\mathfrakm]≠ 0. To prove this, we calculate the index of an Eisenstein ideal I contained in \mathfrakm by computing the order of a cuspidal divisor annihilated by I.

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