Tuesday, December 23, 2014

Motivic Dreams

To show that all L-functions associated to Shimura varieties - thus to any motive defined by a Shimura variety - can be expressed in terms of automorphic L-functions of is weaker, even very much weaker, than to show that all motivic L-functions are equal to such L-functions.  Moreover, although the stronger statement is expected to be valid, there is, so far as I know, no very compelling reason to expect that all motivic L-functions will be attached to Shimura varieties.  - R. Langlands

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