Abstract
We strengthen the compatibility between local and global Langlands correspondences for when is even and . Let be a CM field and a cuspidal automorphic representation of which is conjugate self-dual and regular algebraic. In this case, there is an -adic Galois representation associated to , which is known to be compatible with local Langlands in almost all cases when by recent work of Barnet-Lamb, Gee, Geraghty and Taylor. The compatibility was proved only up to semisimplification unless has Shin-regular weight. We extend the compatibility to Frobenius semisimplification in all cases by identifying the monodromy operator on the global side. To achieve this, we derive a generalization of Mokrane’s weight spectral sequence for log crystalline cohomology.
Citation
Ana Caraiani. "Monodromy and local-global compatibility for $l=p$." Algebra Number Theory 8 (7) 1597 - 1646, 2014. https://doi.org/10.2140/ant.2014.8.1597
Information