Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois representations for even general special orthogonal groups   We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations
corresponding to cohomological cuspidal automorphic representations of certain
quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there
is a Steinberg component and that the archimedean parameters are regular for
the standard representation. This is based on the cohomology of Shimura
varieties of abelian type, of type $D^{\mathbb{H}}$, arising from forms of
$\mathrm{GSO}_{2n}$. As an application, under similar hypotheses, we compute
automorphic multiplicities, prove meromorphic continuation of (half) spin
$L$-functions, and improve on the construction of $\mathrm{SO}_{2n}$-valued
Galois representations by removing the outer automorphism ambiguity.

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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: eess