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
Tuesday, December 23, 2014
Motivic Dreams
Tuesday, December 09, 2014
The Father of Motives
With the passing of Alexander Grothendieck, there is much discussion comparing him to Einstein in the mathematics world. I think it would be more fitting to compare him to Riemann, whose differential geometry made General Relativity possible. Of course, this is meant in a future tense as it is extremely likely Grothendieck's Motives will play a central role in the nonperturbative completion of M-theory.
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