On the rigid cohomology of certain Shimura varieties.
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Peer-reviewed
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Abstract
We construct the compatible system of $\textit{l}$-adic representations associated to a regular algebraic cuspidal automorphic representation of GL$_{n}$ over a CM (or totally real) field and check local-global compatibility for the $\textit{l}$-adic representation away from $\textit{l}$ and finite number of rational primes above which the CM field or the automorphic representation ramify. The main innovation is that we impose no self-duality hypothesis on the automorphic representation.
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Research in the Mathematical Sciences
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2522-0144
2197-9847
2197-9847
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3
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Springer
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Except where otherwised noted, this item's license is described as Attribution 4.0 International
Sponsorship
M.H.'s research received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement number 290766 (AAMOT). K.-W.L.'s research was partially supported by NSF Grants DMS-1069154, DMS-1258962, and DMS-1352216, and by an Alfred P. Sloan Research Fellowship. R.T.'s research was partially supported by NSF Grants DMS-0600716, DMS-1062759, and DMS-1252158, and by the IAS Oswald Veblen and Simonyi Funds. During some of the period when this research was being written up J.T. served as a Clay Research Fellow.