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A Local Analysis of Congruences in the (p, p) Case: Part I

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Compositio Mathematica

Abstract

Given an irreducible, modular, mod p representation p, we analyse the local components at p of newforms f which give rise to it.

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References

  1. Ash, A. and Stevens, G.: Modular forms in characteristic \(\left( \ell \right)\) and special values of L-functions, Duke Math. J.(1986), 849-868.

  2. Carayol, H.: Sur les représentations galoisiennes modulo \(\left( \ell \right)\) attachées aux formes modulaires, Duke Math. J.59 (1989), 785-801.

    Google Scholar 

  3. Diamond, F.: The refined conjecture of Serre, Proc. of Conf. on Elliptic Curves and Modular Forms, Hong Kong 1993, International Press.

    Google Scholar 

  4. Diamond, F. and Taylor, R.: Lifting modular mod \(\left( \ell \right)\) representations, Duke Math. J.74 (1994), 253-269.

    Google Scholar 

  5. Edixhoven, B.: The weight in Serre’s conjectures on modular forms, Inv Math.109 (1992), 563-594.

    Google Scholar 

  6. Gross, B.: A tameness criterion for Galois representations associated to modular forms (mod p), Duke Math. J.61 (1990), 445-517.

    Google Scholar 

  7. Gérardin, P.: Facteurs locaux des algèbres simples de rang 4, I, in Groupes Réductifs et Formes Automorphes, Publ. Math.Paris VII (1978), 37-77.

  8. Hida, H.: Congruences of cusp forms and of the special values of their zeta functions, Inv. Math. 63(1981), 225-261.

    Google Scholar 

  9. Hida, H.: On congruence divisors of cusp forms as factors of the special values of their zeta functions, Inv. Math.64 (1981), 221-262.

    Google Scholar 

  10. Hida, H.: Elementary theory of L-functions and Eisenstein series, LMSST26, Cambridge University Press, 1993.

  11. Khare, C.: Congruences between cusp forms: the (p, p) case, Duke Math. J.80 (1995), 31-68.

    Google Scholar 

  12. Ribet, K.: Congruence relations between modular forms, Proc. ICM, Warsaw (1983), 503-514.

  13. Ribet, K.: Report on mod \(\left( \ell \right)\) representations of Gal(ℚ/ℚ), in Ui. Jannsen et al. (eds.), Motives, Part 2 (1994), 639-676.

  14. Serre, J-P.: Sur les représentations modulaires de degré 2 deGal(ℚ/ℚ), Duke Math. J.54 (1987), 179-230.

    Google Scholar 

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  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India

    Chandrashekhar Khare

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  1. Chandrashekhar Khare
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Khare, C. A Local Analysis of Congruences in the (p, p) Case: Part I. Compositio Mathematica 112, 365–378 (1998). https://doi.org/10.1023/A:1000424731365

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