Local-global compatibility and the action of monodromy on nearby cycles
Local-global compatibility and the action of monodromy on nearby cycles
We strengthen the local-global compatibility of Langlands correspondences for GLn in the case when n is even and l≠p. Let L be a CM field, and let Π be a cuspidal automorphic representation of GLn(AL) which is conjugate self-dual. Assume that Π∞ is cohomological and not “slightly regular,” as defined …