Deo, SV (2022) Effect of increasing the ramification on pseudo-deformation rings. In: Journal de Theorie des Nombres de Bordeaux, 34 (1). pp. 189-216.
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Abstract
Given a continuous, odd, semi-simple 2-dimensional representation of Gℚ,Np over a finite +field of odd characteristic p and a prime ` not dividing Np, we study the relation between the universal deformation rings of the corresponding pseudo-representations for the groups Gℚ,N`p and Gℚ,NƖp. As a related problem, we investigate when the universal pseudo-representation arises from an actual representation over the universal deformation ring. Under some hypotheses, we prove analogues of theorems of Boston and Böckle for the reduced pseudo-deformation rings. We improve these results when the pseudo-representation is unobstructed and p does not divide Ɩ2 − 1. When the pseudo-representation is unobstructed and p divides Ɩ+ 1, we prove that the universal deformation rings in characteristic 0 and p of the pseudorepresentation for Gℚ,NƖp are not local complete intersection rings. As an application of our main results, we prove a big R = T theorem.
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal de Theorie des Nombres de Bordeaux |
| Publisher: | Institut de Mathematique de Bordeaux |
| Additional Information: | The copyright for this article belongs to the Author. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 30 Aug 2022 11:59 |
| Last Modified: | 30 Aug 2022 11:59 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76283 |
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