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 a finite number of rational primes above which the CM field or the automorphic representation ramifies. The main innovation is that we impose no self-duality hypothesis on the automorphic representation.
Bibliographical noteFunding Information:
We would all like to thank the Institute for Advanced Study for its support and hospitality. This project was begun, and the key steps completed, while we were all attending the special IAS special year on ‘Galois representations and automorphic forms’. 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. We would like to thank the referee for their helpful comments. We would also like to thank Elly Gustafsson and Anthony Pulido for help in compiling the index of notations.
© 2016, The Author(s).