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On the ramification of Hecke algebras at Eisenstein primes

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References

  1. Buzzard, K.: Questions about slopes of modular forms. To appear in Astérisque

  2. Fontaine, J.M.: Groupes finis commutatifs sur les vecteurs de Witt. C. R. Acad. Sci., Paris, Sér. A 280, 1423–1425 (1975)

    MathSciNet  Google Scholar 

  3. Fontaine, J.: Il n’y a pas de variété abélienne sur Z. Invent. Math. 81, 515–538 (1985)

    Article  MathSciNet  Google Scholar 

  4. Gerth III, F.: Ranks of 3-class groups of non-Galois cubic fields. Acta Arith. 30, 307–322 (1976)

    MathSciNet  Google Scholar 

  5. Halter–Koch, F.: Einheiten und Divisorenklassen in Galois’schen algebraischen Zahlkörpern mit Diedergruppe der Ordnung 2l für eine ungerade Primzahl l. Acta Arith. 33, 355–364 (1977)

    MathSciNet  Google Scholar 

  6. Lenstra Jr., H.W.: Complete intersections and Gorenstein rings. In: Elliptic curves, modular forms and Fermat’s Last Theorem, ed. by J. Coates, S.T. Yau. Cambridge: International Press 1995

  7. Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math., Inst. Hautes Étud. Sci. 47, 33–186 (1977)

    Article  MathSciNet  Google Scholar 

  8. Mazur, B.: An introduction to the deformation theory of Galois representations. In: Modular forms and Fermat’s last theorem (Boston, MA, 1995), pp. 243–311. New York: Springer 1997

  9. Merel, L.: L’accouplement de Weil entre le sous-groupe de Shimura et le sous-groupe cuspidal de J0(p). J. Reine Angew. Math. 477, 71–115 (1996)

    MathSciNet  Google Scholar 

  10. Oort, F.: Commutative group schemes. Lect. Notes Math., vol. 15. Springer 1966

  11. Oort, F., Tate, J.: Group schemes of prime order. Ann. Sci. Éc. Norm. Supér., IV. Sér. 3, 1–21 (1970)

    MathSciNet  Google Scholar 

  12. Quillen, D.: Higher algebraic K-theory. I. In: Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972). Lect. Notes Math., vol. 341, pp. 85–147. Berlin: Springer 1973

  13. Ramakrishna, R.: On a variation of Mazur’s deformation functor. Compos. Math. 87, 269–286 (1993)

    MathSciNet  Google Scholar 

  14. Raynaud, M.: Schémas en groupes de type (p,...,p). Bull. Soc. Math. Fr. 102, 241–280 (1974)

    MathSciNet  Google Scholar 

  15. Scholz, A.: Idealklassen und Einheiten in kubischen Körpern. Monatsh. Math. Phys. 40, 211–222 (1933)

    Article  MathSciNet  Google Scholar 

  16. Skinner, C., Wiles, A.: Ordinary representations and modular forms. Proc. Natl. Acad. Sci. USA 94, 10520–10527 (1997)

    Article  MathSciNet  Google Scholar 

  17. Wiles, A.: Modular elliptic curves and Fermat’s Last Theorem. Ann. Math. 141, 443–551 (1995)

    Article  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Frank Calegari

  2. Department of Mathematics, Northwestern University, Evanston, IL, 60208-2730, USA

    Matthew Emerton

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  1. Frank Calegari
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  2. Matthew Emerton
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Correspondence to Frank Calegari or Matthew Emerton.

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Calegari, F., Emerton, M. On the ramification of Hecke algebras at Eisenstein primes. Invent. math. 160, 97–144 (2005). https://doi.org/10.1007/s00222-004-0406-z

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