Journal
FINITE FIELDS AND THEIR APPLICATIONS
Volume 93, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2023.102343
Keywords
Global function field; Compatible systems; Galois representations
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In this paper, we provide new instances of the inverse Galois problem over global function fields for finite groups of Lie type. This is achieved by constructing compatible systems of tadic Galois representations valued in a semisimple group G using Galois theoretic and automorphic methods, and then proving that the Galois images are maximal for a set of primes of positive density based on Larsen's classical result on Galois images for compatible systems.
In this paper, we prove new instances of the inverse Galois problem over global function fields for finite groups of Lie type. This is done by constructing compatible systems of tadic Galois representations valued in a semisimple group G using Galois theoretic and automorphic methods, and then proving that the Galois images are maximal for a set of primes of positive density using a classical result of Larsen on Galois images for compatible systems. (c) 2023 Elsevier Inc. All rights reserved.
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