?? galois ... artin ... langlands ... ??? ....

??? given a group in "tannakian" form ... ??? and an action of it that we want to understand ... on some commutative algebra .... ?? how does this manifest ??? ... ???? ....

?? "concretely identify reps of gl(1,Z/20) with functors from "twentieth-root-of-unity completions of Q" to vector spaces" ... ??? ....

??pretty obvious to get a gl(1,Z/20)-torsor from a field with 20t roots of unity ... ??? ....

??? field with ... ??what's that word that i'm trying to think of ... ???some sort of analog of "cyclotomy", but more general ??? .... ?? points of certain order on certain elliptic curve ... ???.... ??? .....

??is the explicitness with which we think we understand absolute abelian galois group of Q not matched for more general absolute abelian galois groups ?? .... ??? ...

????so _do_ we get a dimensional theory from a "level of ramification" ??? .... ???? .... ???? ....

??? "gauss sum" ... ??? ....

?? "frobenius" idea in connection with joyalesque interpretation of zeta function ... ????? .....

??? "invertible module equipped with frame over ... " ... ??? ...