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Jul
8
comment About the restriction of a modular representation to a decomposition subgroup
Ah! So the Weil-Deligne representation is not enough. Interesting.
Jul
8
comment About the restriction of a modular representation to a decomposition subgroup
TL;DR David Loeffler's and Ricky's comments are spot on.
Jul
8
answered About the restriction of a modular representation to a decomposition subgroup
Jul
2
awarded  Curious
Jun
26
awarded  Civic Duty
Jun
26
comment Absolutely irreducible p-adic representation of the absolute Galois group of Q_p
If $\rho$ is continuous and has coefficients in $\mathbb F_{p}$, then its kernel is such an $H$, so that case is no problem.
Jun
26
revised Absolutely irreducible p-adic representation of the absolute Galois group of Q_p
added 4 characters in body
Jun
25
comment What is the probability that a random sequence of polynomials is regular?
I share your expectation, and this seems to follow from the principle of avoidance from sub-varieties, but at the moment, I am unable to write a full proof.
Jun
12
comment Example of a non-smooth irreducible component of the generic fibre of a Hida family?
@Ramsey Not so easily I'm afraid, especially if you want real math but imagine what would happen if it were always possible to resolve the (putative) singularities of the irreducible components of an ordinary Hecke algebra by raising the level at varying auxiliary primes.
Jun
8
answered Some questions related to Iwasawa invariants of elliptic curves
Jun
5
answered Example of a non-smooth irreducible component of the generic fibre of a Hida family?
Jun
3
comment To what extent is it possible to generalise a natural bijection between trees and $7$-tuples of trees, suggested by divergent series?
@TheMaskedAvenger The easy rule of thumb if you do not want to read the paper is that there is a bijection when the statement makes sense in the category in question. This is not the case for your equation because of the -1. The truth is more complicated but only slightly more so, so I recommend reading the article (light reading in the best sense of the term).
May
22
comment Galois representation attached to $3$-torsion points of an elliptic curve
@Robert No, not necessarily.
May
14
comment Universal deformations of modular Galois representations
Look, all I'm pointing out is that a positive answer to your question implies a positive answer for the "different" question, which is already hard (read: false in general) but at least admits a positive answer if you invert $p$. That's why I said you have better chances in that case. But these are just comments: my official answer remains that I think your problem is a hard one.
May
14
comment Universal deformations of modular Galois representations
If your "why" was more of a philosophical nature, to me it all boils down to the fact that the Hecke algebra is "very nice" after inverting $p$ (étale over $\mathbb Q_{p}$, formally smooth in a classical neighborhood...).
May
14
comment Universal deformations of modular Galois representations
Because in that case the results of Coleman-Mazur tell you that you have a locally free sheaf on the eigencurve. Emerton's construction through completed cohomology tells you furthermore that this sheaf comes from the (image through the Jacquet functor of the locally algebraic vectors of the) direct limit of the cohomology of modular curves, so satisfies your requirement. In an affinoid neighborhood of a classical non-critical point, you have an infinitesimal R=T theorem by Kisin identifying this sheaf with the universal deformation, as you wished for.
May
13
comment Universal deformations of modular Galois representations
I thought you might say this. This is why I added the final paragraph. You are in much better shape if you are fine with inverting $p$ and with free sheaves on the corresponding rigid analytic space.
May
13
answered Universal deformations of modular Galois representations
May
9
revised Are dualizable modules finitely generated?
Corrected grammar
May
9
revised Cyclotomic units of abelian extension
Clarified question