On the torsion of Jacobians of principal modular curves of level 3(n) Academic Article

abstract

• We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3 n ) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. 2006 Birkhuser Verlag.

authors

• Papanikolas, Matthew

published proceedings

• ARCHIV DER MATHEMATIK

author list (cited authors)

• Papanikolas, M., & Rasmussen, C.

citation count

• 3

complete list of authors

• Papanikolas, Matthew||Rasmussen, Christopher

publication date

• January 2007

publisher

• Springer Nature  Publisher

published in

• Archiv der Mathematik  Journal

keywords

• Fundamental Group
• Galois Representation
• Modular Curve
• Torsion Points

Digital Object Identifier (DOI)

• 10.1007/s00013-006-1740-8

start page

• 19

end page

• 28

volume

• 88

issue

• 1

URL

• http://dx.doi.org/10.1007/s00013-006-1740-8