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.
Original language | English |
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Pages (from-to) | 217-225 |
Number of pages | 9 |
Journal | Journal of Number Theory |
Volume | 195 |
DOIs | |
State | Published - 1 Feb 2019 |
Keywords
- Galois representations
- Normalized traces
- Pure representations
ASJC Scopus subject areas
- Algebra and Number Theory