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arXiv · 1801.00638

Distinguishing pure representations by normalized traces

Manish Kumar Pandey·Sudhir Pujahari·Jyoti Prakash Saha
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Abstract

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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Manish Kumar Pandey, Sudhir Pujahari, Jyoti Prakash Saha. 2018-01-02. Distinguishing pure representations by normalized traces. https://arxiv.org/abs/1801.00638

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