Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinguishing pure representations by normalized traces   Given two pure representations of the absolute Galois group of an $\ell$-adic
number field with coefficients in $\overline{\mathbb{Q}}_p$ (with $\ell\neq
p$), we show that the Frobenius-semisimplifications of the associated
Weil--Deligne representations are twists of each other by an integral power of
certain unramified character if they have equal normalized traces. This is an
analogue of a recent result of Patankar and Rajan in the context of local
Galois representations.

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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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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: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph