?? "modified ideal class group" .... ?? "modified jacobian" .... ????

?? comma construction here ??? .... ??? in 2-category of dimensional categories ??? .... ??homotopy fiber construction ???? ...... ????

?? hmm, return here to issue of ... ?? how "abelian-like" and/or "abelian-unlike" 2-cat of dimensional categories may be .... ????.....

??? any possibility that progression from abelian class field theory ("artin reciprocity") to non-abelian ("langlands reciprocity") might have to do with moving comma construction / homotopy fiber idea from dimensional doctrine to AG doctrine ???? ..... ???? .... ???? hmmm, possibility of generalized "ramification index" here ???? ......

?? possibility of .... ?? understanding stuff about archimedean ramification in terms of ... ?? extending of "differential calculus" / "blow-up" (???? ... ???relationship and/or non-relationship to homotopy fiber idea ... ??? ... ??? bit about ... ????_(cartier) divisor_ as already blown-up ... ???? .....) from AG to "AG without -1" doctrine ??? ..... ????......

??stuff that todd was trying to tell me about .... trying to unify archimedean with non-archimedean factors of zeta function .... ??? .... ??? "gaussian as self-dual under fourier transform" ... ????? ..... (?? relationship to "poisson summation" ??? ..... ????? ......) ..... "tate's thesis" ... ???...

?? non-archimedean "gaussian" as ... ??? characteristic function of algebraic integers among algebraic numbers ???? .... ???? ....

?? alternation between which of "archimedean" / "non-archimedean" qualifies as "exotic" / "mundane" ... ???? ....

??? ?? "discrete vs continuous" ?? ... ??? ?? "quantum vs classical" ?????? .....
?? input vs output of function subject to fourier transform ... ??? .... ???? function vs measure .... ???? .... ???? ..... ???? ......... ??? ....

?? approaches to class field theory .... ????mentioned by lang (?? see book "algebraic number theory" ... ?? ... ?? "part 2 on class field theory ... about 5 pages of historical overview somewhere ... " ... ?? ...) ??? ...

1 ?? "cohomological" ...

2 ?? "zeta function" .... ??? "tannakian duality" ???? .... (decategorified vs categorified .... ???? ....) ...

3 ?? artin reciprocity ??? ....

4 ?? jugendtraum .... ????? ....

???or something like that ???

(order of listing here as probably completely random ?? ...)