Displaying similar documents to “Galois representations modulo p and cohomology of Hilbert modular varieties”

Congruences between Siegel modular forms on the level of group cohomology

Karsten Buecker (1996)

Annales de l'institut Fourier

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Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the components of the cohomology are independent of the weight parameter. The meaning of depends on a choice of parabolic subgroup of G S p ( 4 ) , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...

A combinatorial interpretation of Serre's conjecture on modular Galois representations

Adriaan Herremans (2003)

Annales de l’institut Fourier

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We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic p , by their counterparts in the theory of modular symbols.