## On $$\ell$$-adic representations attached to modular forms.(English)Zbl 0302.10027

### MSC:

 11F03 Modular and automorphic functions 11F12 Automorphic forms, one variable 11S31 Class field theory; $$p$$-adic formal groups 14G20 Local ground fields in algebraic geometry
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### References:

 [1] Deligne, P.: Formes modulaires et représentationsb-adiques. Séminaire Bourbaki 355, Février 1969. Lecture Notes in Mathematics179. Berlin-Heidelberg-New York: Springer 1971 [2] Dickson, L. E.: Linear groups with an exposition of the Galois field theory. Leipzig: Teubner 1901 · JFM 32.0128.01 [3] Dieudonné, J.: La géométrie des groupes classiques. Berlin-Heidelberg-Göttingen: Springer 1955 · Zbl 0067.26104 [4] Hua, L-K.: Supplement to: On the automorphisms of the classical groups, by J. Dieudonné. AMS Memoirs No. 2. New York: AMS 1951 [5] Katz, N.:p-adic properties of modular schemes and modular forms. International Summer School on Modular Functions; Antwerp, 1972. Lecture Notes in Mathematics350, 69-190, 1973 [6] Ribet, K.: Galois action on division points of abelian varieties with many real multiplications. Harvard thesis, 1971. (To appear in revised form) [7] Serre, J-P.: Abelianl-adic representations and elliptic curves. New York: Benjamin 1968 [8] Serre, J-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Inventiones math.15, 259-331 (1972) · Zbl 0235.14012 [9] Serre, J-P.: Congruences et formes modulaires (d’après H.P.F. Swinnerton-Dyer). Séminaire Bourbaki 416, Juin 1972. Lecture Notes in Mathematics317, 319-338, 1973 [10] Shih, K.: On the construction of Galois extensions of function fields and number fields. Princeton thesis, 1972 [11] Swinnerton-Dyer, H.P.F.: Onl-adic representations and congruences for coefficients of modular forms. International Summer School on Modular Functions; Antwerp, 1972. Lecture Notes in Mathematics350, 1-55, 1973 [12] Wilton, J.R.: Congruence properties of Ramanujan’s function ?(n). Proc. London Math. Soc.31, 1-10 (1928) · JFM 56.0874.02
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