Abstract
Before this conference I had never been to any mathematics gathering where so many people worked as hard or with such high spirits, trying to understand a single piece of mathematics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Azumaya, G., On maximally central algebras, Nagoya Math. J. 2 (1951),119–150.
Boston, N., Explicit deformation of Galois representations., Invent. Math. 103 (1991), 181–196.
Boston, N., A refinement of the Faltings-Serre method„ Number Theory (S. David, ed.), Cambridge Univ. Press, 1995, pp. 61–68.
Boston, N., Mazur, B., Explicit deformations of Galois representations,Algebraic Number Theory — in honor of K. Iwasawa (Coates, Greenberg, Mazur, Satake, eds.), Advanced Studies in Pure Mathematics 17 Academic Press, 1989, pp. 1–21.
Boston, N., Ullom, S., Representations related to CM elliptic curves, Math.Proc. Camb. Phil. Soc. 113 (1993), 71–85.
Bourbaki, N., Algebre, Ch. VIII, Hermann 1958.
Bourbaki, N., Algebre commutative, Ch. I-IV, Masson, 1985.
Byrne, D., Stop Making Sense, Video, The Talking Heads.
Carayol, H., Formes modulaires et représentations Galoisiennes à valeursdans un anneau local complet„ p-adic Monodromy and the Birch-Swinnerton-Dyer Conjecture (Mazur and Stevens, eds.), Contemporary Mathematics 165 Amer. Math. Soc., 1994, pp. 213–237.
Coleman, R., P-adic Banach spaces and families of modular forms, Invent.math. (to appear).
Conrad, B., The flat deformation functor,(this volume).
Curtis, C., Reiner, I., Representation theory of finite groups and associative algebras, Wiley, 1962.
Darmon, H., Diamond, F., Taylor, R., Fermat’s Last Theorem, Current De-velopments in Mathematics (Bott, Jaffe, Yau, eds.), (1995), International Press., 1995, pp. 1–108.
Doran, C., Wong, S., The deformation theory of Galois representations,in preparation..
Fontaine, J.-M., Groupes p-divisibles sur les corps locaux, Astérisque, Soc. Math. de France 47–48 (1977).
Fontaine, J.-M., Groupes finis commutatifs sur les vecteurs de Witt, C.R. Acad. Sci. Paris 280 (1975), 1423–1425.
Fontaine, J.-M., Laffaille, Construction de représentations p-adiques, Ann. Scient. E.N.S. 15 (1982), 547–608.
Fontaine, J.-M., Mazur, B., Geometric Galois representations, Proceedings of the Conference on Elliptic Curves and Modular Forms (Coates, Yau, eds.), Hong Kong, Dec. 18–21 1993, International Press., 1995, pp. 47–78.
Frobenius, G., Über die Primfactoren der Gruppendeterminante, Sitz. Preuss. Akad. Berlin (1896), 1343–1382 (pp. 38–77 in Ges. Abh. III).
Gouvêa, F. Arithmetic of p-adic modular forms,Lecture Notes in Math. 1304 Springer-Verlag, 1988.
Gouvêa, F., Mazur, B. Families of modular eigenforms, Mathematics of Computation 58 (1992), 793–805.
Grothendieck, A., Éléments de Géométrie Algébrique IV (Étude locale des schémas et des morphismes de schémas), Publ. Math. IHES 20 (1964).
Hida, H., Elementary theory of L-functions and Eisenstein series, London Math. Soc. (1993).
Hartshorne, R., Algebraic Geometry, Springer-Verlag, 1977.
Knus, M.-A., Ojanguren, M., Théorie de la descente et algébres d’Azumaya, Lecture Notes in Math 389, Springer-Verlag, 1974.
Lubotzky, A., Magid, A., Varieties fo representations of finitely generated groups, Memoirs of the A.M.S. 58 (1985).
Lenstra, H., de Smit, B., Explicit construction of universal deformation rings, (this volume).
Matsumura, H., Commutative Algebra, W.A. Benjamin Co., 1970.
Mazur, B., Deforming Galois representations, Galois groups over Q (Ihara, Ribet, Serre, eds.), MSRI Publications 16, Springer-Verlag, 1989, pp. 385–437.
Mazur, B.Two-dimensional p-adic Galois representations unramified away from p, Compositio Math 74 (1990), 115–133.
An “infinite fern” in the universal deformation space of Galois representations, Proceedings of the Journées Arithmeétiques, held in Barcelona, July 1995. (to appear).
Mazur, B., Tilouine, J., Représentations galoisiennes, différentielles de Kähler et conjectures principales, Publ. Math. IHES 71 (1990), 65–103.
Nyssen, L., Pseudo-représentations, preprint 1994.
Procesi, C., Rings with Polynoimal Identities, Dekker, 1973.
Procesi, C., Representations of algebras, Israel J. Math. 19 (1974), 169–182.
Ramakrishna, R., On a variation of Mazur’s deformation functor, Com-positio Math 87 (1993), 269–286.
Rouquier, R., Caractérisation des caractéres et pseudo-caractéres, preprint 1995.
Schlessinger, M., Functors on Artin rings, Trans. A.M.S. 130 (1968), 208–222.
Serre, J.-P., Corps Locaux, 2nd ed., Hermann, 1968.
Serre, J.-P.,Représentations linéaires sur des anneaux locaux (d’aprés Cara-yol), preprint, 1995.
Serre, J.-P.,Points d’ordre fini des courbes elliptiques, Invent. Math. 15 (1972),259–331.
Taylor, R., Galois representations associated to Siegel modular forms of low weight, Duke Math. J. 63 (1991), 281–332.
Taylor, R., Wiles, A., Ring-theoretic properties of certain Hecke algebras,Annals of Math. 141 (1995), 553–572.
Wiles, A., Modular elliptic curves and Fermat’s Last Theorem, Annals of Math. 141 (1995), 443–551.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mazur, B. (1997). An Introduction to the Deformation Theory of Galois Representations. 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_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1974-3_8
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