Startseite Rational torsion of generalized Jacobians of modular and Drinfeld modular curves
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Rational torsion of generalized Jacobians of modular and Drinfeld modular curves

  • Fu-Tsun Wei und Takao Yamazaki EMAIL logo
Veröffentlicht/Copyright: 20. Januar 2019

Abstract

We consider the generalized Jacobian J~ of the modular curve X0(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 -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.


Communicated by Freydoon Shahidi


Award Identifier / Grant number: 105-2115-M-007-018-MY2

Award Identifier / Grant number: 107-2628-M-007-004-MY4

Award Identifier / Grant number: 15K04773

Funding statement: The first author is supported by Ministry of Science and Technology, Taiwan (grant number 105-2115-M-007-018-MY2 and 107-2628-M-007-004-MY4). The second author is supported by Japan Society for the Promotion of Science KAKENHI Grant (grant number 15K04773).

Acknowledgements

We thank the referee for careful reading which helped improving our manuscript.

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Received: 2018-06-13
Revised: 2018-11-28
Published Online: 2019-01-20
Published in Print: 2019-05-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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