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The Flat Deformation Functor

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Modular Forms and Fermat’s Last Theorem

Abstract

Let E /Q be a semistable elliptic curve and p a prime. In the proof that E is modular, properties of the local representation

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References

  1. M. Atiyah, I. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.

    Google Scholar 

  2. S. Bloch, K. Kato, L-functions and Tamagawa Numbers of Motives, The Grothendieck Festschrift, vol. I Birkhäuser, 1990, pp. 333–400.

    Google Scholar 

  3. S. Bosch, W. Lütkebohmert, M. Raynaud, Néron Models, Springer-Verlag, 1980.

    Google Scholar 

  4. B. Conrad, Assorted Extras and Tidbits, notes for lectures at Princeton, Spring, 1995.

    Google Scholar 

  5. B. Conrad, Background Notes on p-divisible Groups over Local Fields, notes for lectures in Seminar on Assorted Topics, Princeton, Fall, 1995.

    Google Scholar 

  6. B. Conrad, Filtered Modules, Galois Representations, and Big Rings, notes for lectures at Princeton, Fall, 1994.

    Google Scholar 

  7. B. Conrad, Finite Honda Systems and Supersingular Elliptic Curves, thesis, Princeton University, 1996.

    Google Scholar 

  8. H. Darmon, F. Diamond, R. Taylor, Fermat’s Last Theorem, preprint.

    Google Scholar 

  9. B. de Smit, K. Rubin, R Schoof, Criteria for Complete Intersections, this volume.

    Google Scholar 

  10. F. Diamond, On Deformation Rings and Hecke Rings, preprint.

    Google Scholar 

  11. F. Diamond, K. Ribet, e-adic Modular Deformations and Wiles’s “Main Conjecture”, this volume.

    Google Scholar 

  12. J.-M. FontaineGroupes p-divisible sur les corps locaux, Astérisque 47–48, Soc. Math. de France, 1977.

    Google Scholar 

  13. J.-M. FontaineGroupes finis commutatifs sur les vecteurs de Witt, C.R. Acad. Sci. 280 (1975), pp. 1423–1425.

    MathSciNet  MATH  Google Scholar 

  14. J.-M. Fontaine, G. LaffailleConstruction de représentations padiques, Ann. Sci. E.N.S. (1982), pp. 547–608.

    Google Scholar 

  15. J.-M. Fontaine, B. Mazur, Geometric Galois Representations in Elliptic Curves, Modular Forms, and Fermat’s Last Theorem, International Press 1995, pp. 41–78.

    Google Scholar 

  16. A. Grothendieck, Éléments de Géométrie Algébrique, Math Publ. IRES.

    Google Scholar 

  17. A. Grothendieck, Séminaire de Géométrie Algébrique 2.

    Google Scholar 

  18. A. Grothendieck, Séminaire de Géométrie Algébrique 7.

    Google Scholar 

  19. P. Hilton, U. StammbachA Course in Homological Algebra, GTM 4, Springer-Verlag, 1970.

    Google Scholar 

  20. N. Katz, B. Mazur, Arithmetic Moduli of Elliptic Curves, Princeton Univ. Press, Princeton, 1985.

    Google Scholar 

  21. H. MatsumuraCommutative Ring Theory, Cambridge Univ. Press, 1986.

    MATH  Google Scholar 

  22. B. Mazur, Deforming Galois Representations in Galois Groups over Q, pp. 385–437.

    Google Scholar 

  23. B. Mazur, An Introduction to the Deformation Theory of Galois Representations, this volume.

    Google Scholar 

  24. D. MumfordAbelian Varieties, Oxford University Press, 1970.

    Google Scholar 

  25. T. OdaThe first DeRham Cohomology and Dieudonne Modules, Ann. Sci. E.N.S., 5e série t.2, 1969, pp. 63–135.

    MathSciNet  MATH  Google Scholar 

  26. F. Oort, J. TateGroup Schemes of Prime Order, Ann. Sci. E.N.S. (1970), pp. 1–21.

    Google Scholar 

  27. R. RamakrishnaOn a Variation of Mazur’s Deformation Functor, Compositio Math. (3) 87 (1993), pp. 269–286.

    MathSciNet  MATH  Google Scholar 

  28. M. RaynaudSchémas en groupes de type (p, p,…,p), Bull. Soc. Math. France 102 (1974), pp. 241–280.

    MathSciNet  MATH  Google Scholar 

  29. J-P. Serre, Local Fields, GTM 67, Springer-Verlag, 1979.

    MATH  Google Scholar 

  30. J-P. Serre, Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Inv. Math. 15 (1972), pp. 259–331.

    Article  MATH  Google Scholar 

  31. J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

    MATH  Google Scholar 

  32. J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer-Verlag, 1993.

    Google Scholar 

  33. J. Tate, p-divisible groups in Proceedings of a Conference on Local Fields (Driebergen), pp. 158–183, 1966.

    Google Scholar 

  34. J. Tate, Finite Flat Group Schemes,this volume.

    Google Scholar 

  35. R. Taylor, A. Wiles, Ring-theoretic Properties of Certain Hecke Algebras, Annals of Mathematics (3) 141 (1995), pp. 553–572.

    Article  MathSciNet  MATH  Google Scholar 

  36. J. Tilouine, Hecke Algebras and the Gorenstein Property, this volume.

    Google Scholar 

  37. L. Washington, Galois Cohomology,this volume.

    Google Scholar 

  38. A. Wiles, Modular Elliptic Curves and Fermat’s Last Theorem, Annals of Mathematics (3) 141 (1995), pp. 443–551.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Brian Conrad
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06268, USA

    Gary Cornell

  2. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Joseph H. Silverman

  3. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Glenn Stevens

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© 1997 Springer Science+Business Media New York

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Conrad, B. (1997). The Flat Deformation Functor . In: Cornell, G., Silverman, J.H., Stevens, G. (eds) Modular Forms and Fermat’s Last Theorem. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1974-3_13

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  • DOI: https://doi.org/10.1007/978-1-4612-1974-3_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98998-3

  • Online ISBN: 978-1-4612-1974-3

  • eBook Packages: Springer Book Archive

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