On the density of modular points in universal deformation spaces, by Gebhard Boeckle

Based on comparison theorems for Hecke algebras and universal deformation rings with strong restrictions at the critical prime l, as provided by the results of Wiles, Taylor, Diamond, Conrad et al., we prove under rather general conditions that the corresponding universal deformation spaces with no restrictions at l can be identified with certain Hecke algebras of Katz' generalized cuspidal eigenforms as conjectured by Gouv^ea, thus generalizing previous work of Gouv^ea and Mazur.

Along the way, we show that the universal deformation spaces we consider are complete intersections, generically smooth and flat over Z_l of relative dimension three, in which the modular points form a Zariski dense subset.

Gebhard Boeckle <boeckle@math.ethz.ch>