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2017 Generalized Kuga–Satake theory and good reduction properties of Galois representations
Stefan Patrikis
Algebra Number Theory 11(10): 2397-2423 (2017). DOI: 10.2140/ant.2017.11.2397


In previous work, we described conditions under which a single geometric representation Γ F H ( ¯ ) of the Galois group of a number field F lifts through a central torus quotient H ˜ H to a geometric representation. In this paper, we prove a much sharper result for systems of -adic representations, such as the -adic realizations of a motive over F , having common “good reduction” properties. Namely, such systems admit geometric lifts with good reduction outside a common finite set of primes. The method yields new proofs of theorems of Tate (the original result on lifting projective representations over number fields) and Wintenberger (an analogue of our main result in the case of a central isogeny H ˜ H ).


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Stefan Patrikis. "Generalized Kuga–Satake theory and good reduction properties of Galois representations." Algebra Number Theory 11 (10) 2397 - 2423, 2017.


Received: 30 April 2017; Revised: 8 August 2017; Accepted: 6 September 2017; Published: 2017
First available in Project Euclid: 1 February 2018

zbMATH: 06825455
MathSciNet: MR3744361
Digital Object Identifier: 10.2140/ant.2017.11.2397

Primary: 11F80
Secondary: 11R37

Keywords: Galois representations , Kuga–Satake construction

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.11 • No. 10 • 2017
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