Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Demostraci\'on simplificada de la Conjetura de Modularidad de Serre
  (carta)   We explain in this letter how using a recent Modularity Lifting Theorem
proved by Lue Pan the proofs of Serre's Modularity Conjecture over $\mathbb{Q}$
given by Khare-Wintenberger and the author can be greatly simplified. The main
difference with the previous proofs is that neither the process of "weight
reduction" developed by Khare in his proof of the level 1 case nor the
alternative method of "weight reduction via Galois conjugation" developed by
the author are required: weight reduction can now be obtained just with two
applications of Pan's result, together with a Lemma that guarantees that the
residual representations in the last two steps are not in the bad-dihedral
case.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg