On the density of modular representations, by Fernando Q. Gouvêa and Barry Mazur

This paper has appeared in Computational perspectives on number theory (Chicago, IL, 1995), 127-142, AMS/IP Stud. Adv. Math. 7, Amer. Math. Soc., Providence, RI, 1998 and so the dvi version has been removed. In this article, which is to appear in the proceedings of the Atkin conference held in Chicago in September of 1995, we explore the problem of describing the universal deformation of a Galois representation in terms of modular forms by considering a very special case: we assume a "level p" situation, "non-critical slope", and an "unobstructed" deformation problem. These assumptions allow us to give a "modular" description of the universal deformation ring, and to relate it to a certain Hecke algebra. The dvi file requires the "xypic" fonts.

Fernando Q. Gouvêa and Barry Mazur <fqgouvea@colby.edu>