Monodromy and Local-global Compatibility for L = P

  title={Monodromy and Local-global Compatibility for L = P},
  author={Ana Caraiani},
  • Ana Caraiani
  • Published 2012
We strengthen the compatibility between local and global Langlands correspondences for GLn when n is even and l = p. Let L be a CM field and Π a cuspidal automorphic representation of GLn(AL) which is conjugate self-dual and regular algebraic. In this case, there is an l-adic Galois representation associated to Π, which is known to be compatible with local Langlands in almost all cases when l = p by recent work of Barnet-Lamb, Gee, Geraghty and Taylor. The compatibility was proved only up to… CONTINUE READING

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