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
Tuesday, December 09, 2014
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.