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On the rigid cohomology of certain Shimura varieties.

Published version
Peer-reviewed

Change log

Authors

Harris, Michael 
Lan, Kai-Wen 
Taylor, Richard 
Thorne, Jack 

Abstract

We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of GLn over a CM (or totally real) field and check local-global compatibility for the l-adic representation away from 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.

Description

Keywords

4902 Mathematical Physics, 4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Research in the Mathematical Sciences

Conference Name

Journal ISSN

2522-0144
2197-9847

Volume Title

3

Publisher

Springer
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.