Galois representations associated with a non-selfdual automorphic representation of GL(3)

Abstract

In 1994, van Geemen and Top constructed a non-selfdual motive of rank three over Q conjecturally associated with a cuspidal non-selfdual automorphic representation of GL 3 (A Q ) of level Γ 0 (128). They experimentally confirmed the coincidence of the local L-factors at finitely many primes using computer. In this paper, we shall prove the coincidence of the local L-factors at every prime. To show this, we use the recent results of Harris-Lan-Taylor-Thorne and Scholze on the construction of Galois representations, and Grenié's results to compare three-dimensional 2-adic Galois representations. We also prove the local-global compatibility at p = 2, including the case p = ℓ.