Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality

@article{Hansen2014UniversalET,
  title={Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality},
  author={D. Hansen},
  journal={arXiv: Number Theory},
  year={2014}
}
  • D. Hansen
  • Published 2014
  • Mathematics
  • arXiv: Number Theory
Using the overconvergent cohomology modules introduced by Ash and Stevens, we construct eigenvarieties associated with reductive groups and establish some basic geometric properties of these spaces, building on work of Ash-Stevens, Urban, and others. We also formulate a precise modularity conjecture linking trianguline Galois representations with overconvergent cohomology classes. In the course of giving evidence for this conjecture, we establish several new instances of \emph{p-}adic Langlands… Expand

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