Modular representations on some Riemann-Roch spaces of modular curves X(N)
Algebraic Geometry
2007-05-23 v1 Representation Theory
Abstract
We compute the PSL(2,N)-module structure of the Riemann-Roch space L(D), where D is an invariant non-special divisor on the modular curve X(N), with N > 5 prime. This depends on a computation of the ramification module, which we give explicitly. These results hold for characteristic p if X(N) has good reduction mod p and p does not divide the order of PSL(2,N). We give as examples the cases N=7, 11, which were also computed using GAP. Applications to AG codes associated to this curve are considered, and specific examples are computed using GAP and MAGMA.
Cite
@article{arxiv.math/0502586,
title = {Modular representations on some Riemann-Roch spaces of modular curves X(N)},
author = {David Joyner and Amy Ksir},
journal= {arXiv preprint arXiv:math/0502586},
year = {2007}
}
Comments
49 pages, talk given at AMS Atlanta Algorithmic Algebraic Geometry seesion