## Duke Mathematical Journal

### Galois representations associated to Siegel modular forms of low weight

Richard Taylor

#### Article information

Source
Duke Math. J. Volume 63, Number 2 (1991), 281-332.

Dates
First available in Project Euclid: 20 February 2004

http://projecteuclid.org/euclid.dmj/1077295922

Digital Object Identifier
doi:10.1215/S0012-7094-91-06312-X

Mathematical Reviews number (MathSciNet)
MR1115109

Zentralblatt MATH identifier
0810.11033

#### Citation

Taylor, Richard. Galois representations associated to Siegel modular forms of low weight. Duke Math. J. 63 (1991), no. 2, 281--332. doi:10.1215/S0012-7094-91-06312-X. http://projecteuclid.org/euclid.dmj/1077295922.

#### References

• [A] A. N. Andrianov, Quadratic forms and Hecke operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 286, Springer-Verlag, Berlin, 1987.
• [BR] D. Blasius and D. Ramakrishnan, Maass forms and Galois representations, Galois groups over $\bf Q$ (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer, New York, 1989, pp. 33–77.
• [C] C.-L. Chai, Compactification of Siegel moduli schemes, London Mathematical Society Lecture Note Series, vol. 107, Cambridge University Press, Cambridge, 1985.
• [CF] G. Faltings and C.-L. Chai, Degeneration of abelian varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 22, Springer-Verlag, Berlin, 1990.
• [D] P. Deligne, June 1968, letter to Serre, dated 24.
• [DS] P. Deligne and J.-P. Serre, Formes modulaires de poids $1$, Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530 (1975).
• [Ha] M. Harris, Automorphic forms and the cohomology of vector bundles on Shimura varieties, Automorphic forms, Shimura varieties, and $L$-functions, Vol. II (Ann Arbor, MI, 1988) eds. L. Clozel and J. S. Miline, Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, pp. 41–91.
• [He] G. Henniart, Formes de Maass et représentations galoisiennes (d'après Blasius, Clozel, Harris, Ramakrishnan et Taylor), Astérisque (1989), no. 177-178, Exp. No. 711, 277–302, Sém. Bourbaki, Société Mathématique de France.
• [J] N. Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964.
• [JS] H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815.
• [MW] B. Mazur and A. Wiles, Class fields of abelian extensions of $\bf Q$, Invent. Math. 76 (1984), no. 2, 179–330.
• [P] C. Procesi, The invariant theory of $n\times n$ matrices, Advances in Math. 19 (1976), no. 3, 306–381.
• [Se] J.-P. Serre, Abelian $l$-adic representations and elliptic curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, W. A. Benjamin, Inc., New York-Amsterdam, 1968.
• [Sh] G. Shimura, On modular correspondences for $Sp(n,\,Z)$ and their congruence relations, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 824–828.
• [T1] R. Taylor, Congruences between Siegel modular forms, preprint.
• [T2] R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), no. 2, 265–280.
• [T3] R. Taylor, On congruences between modular forms, thesis, Princeton University, 1988.
• [T4] R. Taylor, October 1988, letter to Blasius, dated 16.
• [W] A. Wiles, On ordinary $\lambda$-adic representations associated to modular forms, Invent. Math. 94 (1988), no. 3, 529–573.