I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some recent important work of Coleman, it is something one can actually produce! The infinite fern'' is joint work with F.Q. Gouvea, and will be the subject of slightly more systematic study in a future paper in which some consequences of its existence will be discussed. Although the infinite fern'' which appears in the last section of these notes is hardly as profound a point-set topological object as some of the classic constructions of R.H. Bing, I would like to think that he might have nevertheless enjoyed it. I want to dedicate this article to him, in appreciation of his mathematics and of his energetic enthusiasm.
@article{urn:eudml:doc:40396,
title = {An infinite ferm in the universal deformation space of Galois representations.},
journal = {Collectanea Mathematica},
volume = {48},
year = {1997},
pages = {155-193},
zbl = {0865.11046},
mrnumber = {MR1464022},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40396}
}
Mazur, B. An infinite ferm in the universal deformation space of Galois representations.. Collectanea Mathematica, Tome 48 (1997) pp. 155-193. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40396/