@article{ae193012b06a453895d084c255552408,
title = "Distinguishing pure representations by normalized traces",
abstract = "Given two pure representations of the absolute Galois group of an ℓ-adic number field with coefficients in Q‾p (with ℓ≠p), we show that the Frobenius-semisimplifications of the associated Weil–Deligne representations are twists of each other by an integral power of a 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.",
keywords = "Galois representations, Normalized traces, Pure representations",
author = "Pandey, {Manish K.} and Sudhir Pujahari and Saha, {Jyoti Prakash}",
note = "Funding Information: The first author would like to thank Prof. B. Ramakrishnan for his encouragement, during the work of this paper the author is supported by the Infosys scholarship. The second author would like to thank the Harish-Chandra Research Institute, where he was a post-doctoral fellow while working on a preliminary version of this paper. The third author would like to thank Prof. C.S. Dalawat for an invitation to the Harish-Chandra Research Institute during June, 2017 when this work was initiated. He is grateful to the institute for providing a warm hospitality. During the final stage of the work, he was supported by a postdoctoral fellowship at the Ben-Gurion University of the Negev, offered by the Israel Science Foundation Grant number 87590011 of Prof. Ishai Dan-Cohen. We are grateful to the referee for making valuable comments and providing detailed remarks that improved the clarity of the exposition. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2019",
month = feb,
day = "1",
doi = "10.1016/j.jnt.2018.06.003",
language = "English",
volume = "195",
pages = "217--225",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
}