Rational torsion of generalized Jacobians of modular and Drinfeld modular curves

Fu Tsun Wei, Takao Yamazaki

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the generalized Jacobian J of the modular curve X 0 (N) of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the Q-rational torsion points on J up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on J and its Eisenstein property.

Original languageEnglish
Pages (from-to)647-659
Number of pages13
JournalForum Mathematicum
Volume31
Issue number3
DOIs
Publication statusPublished - 2019 May 1

Keywords

  • Cuspidal divisor group
  • Drinfeld modular curves
  • Eisenstein ideal
  • Generalized Jacobian
  • Modular curves

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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