P-adic Banach Spaces and Families of Modular Forms, by Robert F. Coleman
This paper has appeared in Invent. Math. 127 (1997) no. 3, 417-479, and so
the dvi version has been removed. This paper is a new version of preprint 0007.
In this paper, we prove qualitative versions of the Gouv\^ea-Mazur
conjectures on families of modular forms of non-zero slope. We do
this by first extending Serre's $p$-adic Banach space theory from spaces
over complete normed fields to modules over complete normed algebras.
Robert F. Coleman <email@example.com,edu>