Congruences between Siegel modular forms on the level of group cohomology

Karsten Buecker

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 4, page 877-897
  • ISSN: 0373-0956

Abstract

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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 ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary 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 classes of parabolic subgroups.

How to cite

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Buecker, Karsten. "Congruences between Siegel modular forms on the level of group cohomology." Annales de l'institut Fourier 46.4 (1996): 877-897. <http://eudml.org/doc/75204>.

@article{Buecker1996,
abstract = {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 ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of $GSp(4)$, giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible classes of parabolic subgroups.},
author = {Buecker, Karsten},
journal = {Annales de l'institut Fourier},
keywords = {vector-valued Siegel modular forms; congruences of Hecke eigenvalues; group cohomology},
language = {eng},
number = {4},
pages = {877-897},
publisher = {Association des Annales de l'Institut Fourier},
title = {Congruences between Siegel modular forms on the level of group cohomology},
url = {http://eudml.org/doc/75204},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Buecker, Karsten
TI - Congruences between Siegel modular forms on the level of group cohomology
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 4
SP - 877
EP - 897
AB - 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 ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of $GSp(4)$, giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible classes of parabolic subgroups.
LA - eng
KW - vector-valued Siegel modular forms; congruences of Hecke eigenvalues; group cohomology
UR - http://eudml.org/doc/75204
ER -

References

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  14. [Pan] A.A. PANCHISHKIN, Non-Archimedean L-functions of Siegel and Hilbert modular forms, LNM 1471, Springer, 1991. Zbl0732.11026MR93a:11044
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