Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstruction criteria for modular deformation problems   For a newform $f=\sum a_n q^n$ of weight $k \geq 3$ and a prime $\lambda$ of
$\mathbf{Q}(a_n)$, the deformation problem for its associated mod $\lambda$
Galois representation is unobstructed for all primes outside some finite set.
Previous results gave an explicit bound on this finite set for $f$ of
squarefree level; we modify this bound and remove the squarefree hypothesis. We
also show that if the $\lambda$-adic deformation problem for $f$ is
unobstructed, then $f$ is not congruent mod $\lambda$ to a newform of lower
level.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph