A combinatorial version of Serre's conjecture on modular Galois representations
by
Adriaan Herremans
K.U. Leuven

The eigenvalues of the Hecke algebra acting on the space of cusp forms (of some given conductor, weight and character) are the eigenvalues of the Hecke algebra acting on some suitable singular cohomology group, for which an explicit combinatorial description can be obtained from the theory of modular symbols. This allows one to reformulate Serre's conjecture on modular Galois representations in purely combinatorial terms (not involving modular forms).

Date received: February 14, 2001