Finiteness of Selmer groups and deformation rings, by Chandrashekhar Khare, Ravi Ramakrishna

We prove the finiteness of certain Selmer groups that can be interpreted as tangent spaces of certain morphisms of deformation rings of 2 dimensional mod p representations of the Galois group of the rationals. We also deduce some consequences for the structure of these deformation rings that are implied by well-known conjectures of Fontaine and Mazur.

Chandrashekhar Khare, Ravi Ramakrishna <shekhar@math.tifr.res.in, ravi@math.cornell.edu>