68 research outputs found
Ordinary deformations are unobstructed in the cyclotomic limit
The deformation theory of ordinary representations of the absolute Galois
groups of totally real number fields (over a finite field ) has been studied
for a long time, starting with the work of Hida, Mazur and Tilouine, and
continued by Wiles and others. Hida has studied the behaviour of these
deformations when one considers the -cyclotomic tower of extensions of the
field. In the limit, one obtains a deformation ring classifying the ordinary
deformations of the (Galois group of) the -cyclotomic extension. We show
that if this ring in Noetherian (a natural assumption considered by Hida) it is
free over the ring of Witt vectors of . This however imposes natural
conditions on certain -invariants
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