Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-big subgroups for l large   Lifting theorems form an important collection of tools in showing that Galois
representations are associated to automorphic forms. (Key examples in dimension
n>2 are the lifting theorems of Clozel, Harris and Taylor and of Geraghty.) All
present lifting theorems for n>2 dimensional representations have a certain
rather technical hypothesis---the residual image must be `big'. The aim of this
paper is to demystify this condition somewhat.
  For a fixed integer n, and a prime l larger than a constant depending on n,
we show that n dimensional mod l representations which fail to be big must be
of one of three kinds: they either fail to be absolutely irreducible, are
induced from representations of larger fields, or can be written as a tensor
product including a factor which is the reduction of an Artin representation in
characteristic zero. Hopefully this characterization will make the bigness
condition more comprehensible, at least for large l.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin