2000 character limit reached
On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields (2312.01551v2)
Published 4 Dec 2023 in math.NT and math.RT
Abstract: Let $F$ be a CM field. In this paper, we prove the local-global compatibility for cohomological cuspidal automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ at $p \neq l$ by using certain potential automorphy theorems in some cases including higher dimensional cases. Moreover, we also prove the Ramanujan conjecture for cohomological cuspidal automorphic representations of $\mathrm{GL}_2(\mathbb{A}_F )$.