?? categorified riemann zeta function ....

?? assign to each finite set set of semi-simple comm ring structures on it ... ?? n! such structures on n .... ???? ....

??? then would like .... ???? corresponding vsp-valued structure type ...... ????? ..... ?? so would give same decategorification .... ??? ....

?? assigining n!-dim vsp to n .... ??? so cardinality k^[n!] .... ???? ....

?? "structure type where structure on n is assignment to each semi-simple comm ring structure on n of map from its components to 3" ..... ??????

?? for example n = 4 .... ???? 12 one-component structures and 12 two-component ones .... ????? .... 3^12 * (3^2)^12 .... ?? whereas i was naively expecting 3^24 ???? ...... ???? just how screwed up are things here ???? .....

??? dirichlet-exponentiate structure type given by ??? field structure augmented by ...... ????? ..... ????? ............. ?????

spec(number ring) X spec(finite field) -> z^k

?? given alg ab gp, hom into it from spectrums of finite fields ... then dirichet-exponetiate that thing .... ??? .... ??? .....


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