Modular representations on some Riemann-Roch spaces of modular curves X(N)

2005/02/28 by David Joyner, Joyner, David, Amy Ksir +1
Mathematics · #14G35 #14H37 #14Q05 #20C10 #94B27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14G35 #msc:14H37 #msc:14Q05 #msc:20C10 #msc:94B27

paper · pdf · doi:10.48550/arxiv.math/0502586

49 pages, talk given at AMS Atlanta Algorithmic Algebraic Geometry seesion

arxiv created 2005/02/28 · arxiv updated 2009/12/01

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.

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