Modular representations on some Riemann-Roch spaces of modular curves X(N)
Abstract
Description
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.
49 pages, talk given at AMS Atlanta Algorithmic Algebraic Geometry seesion
49 pages, talk given at AMS Atlanta Algorithmic Algebraic Geometry seesion