Abstract
In [6] Mazur showed how there is a “versal deformation” parametrising the collection of p-adic representations of a profinite group G lifting a given representation \(\bar p\,:\,G\, \to \,G{L_2}\,\left( {{\mathbb{F}_p}} \right).\) Of particular interest are the \(\bar p\,\) associated to modular forms and elliptic curves in which G is the Galois group of a maximal algebraic extension of Q unramified outside a finite set S of rational primes containing p.
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Bibliography
N. Boston.- Deformation Theory of Galois Representations, Harvard Ph. D. Thesis, 1987.
N. Boston and B. Mazur - Explicit universal deformations of Galois representations, to appear in volume 17, Advanced Studies in Pure Mathematics.
A.Brumer - Galois groups of extensions of algebraic number fields with given ramification, Michigan Math. J. 13 (1966), 33–40.
P. Deligne.- Formes modulaires et représentations ℓ-adiques, Sém. Bourb. 355 (1969); LNM 179 (1971) Berlin-Heidelberg-New York.
H. Koch - Galoissche Theorie der p-Erweiterungen, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
B. Mazur.- Deforming Galois representations, to appear in the Proceedings of the March 1987 Workshop on Galois groups over Q held at MSRI, Berkeley, California.
B. Mazur and A. Wiles- On p-adic analytic families of Galois representations, Comp. Math. 59 (1986), 231–264.
J. Neukirch- Uber das Einbettungsproblem der algebraischen Zahlentheorie, Inv. Math. 21 (1973), 59–116.
Neumann.- On p-closed number fields and an analogue of Riemann’s existence theorem, In Algebraic Number Fields, Academic Press., London 1977 (Frohlich ed.), 625–647.
D. Robinson.- A Course in the Theory of Groups, Springer-Verlag, Berlin-Heidelberg, New York, 1982.
P. Swinnerton-Dyer.- On i-adic representations and congruences for coefficients of modular forms, LNM 350, Springer-Verlag, Berlin-Heidelberg-New York, 1973, 1–55.
S. Wagstaff- The irregular primes to 125000, Math. Comp. 32 (1978), 583–591.
L. Washington - Introduction to Cyclotomic Fields, Springer-Verlag, Berlin-Heidelberg-New York, 1982.
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© 1990 Birkhäuser Boston
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Boston, N. (1990). Deformations of Galois Representations Associated to the Cusp Form △. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1987–88. Progress in Mathematics, vol 81. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3460-9_3
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