?? "incestuous" nature of "l-function" ??? .... ??? coefficients may themselves undergo galois action ... ??? ... ???? .....
?? "fourier duality proof of quadratic reciprocity" .... ??? .... ????? .... ??? ....
?? lambda .... ... q .... .... ????? .... ???? ....
?? character of perm rep .... trace .... fixed points .... ???? ....
?? motive _as_ quasicoherent sheaf over some sort of "galois stack" ??? ... ???? ...
?? trying to set up "square" here .... ??? ....
?? "set-valued galois rep" .... ???? given by (for example) homming gaussian integers into q-bar .... ???? ..... ?? then decompose this (??2d ...) perm rep into irreps .... ?? perhaps over f_q for some q ??? ... ???? ... ??? hopf alg interpretation ??? .... of ... ??? ... ?? perm rep over f_q .... ???? ....
?? comm ring r st [r,q-bar] = (naturally ... ??? ...) 1 + [z[i],q-bar] + 1 ... ????? .... ??? z X z[i] X z ... ??? .... ?? making this into bistable hopf alg ?? ... ??? then decomposing it wrt tensor product of bistable hopf algs ?? ... ??? ..... ???? ....
?? fourier dual of z/2 ??? ....
?? z[x]/x^2-1 ...... ?????? ....
?? confusion ..... ???? ......
?? z X z X z X z[i] X z[i] X z[i] ..... ???? .....
?? z[x]/x^2+x+1 # ... ???? ....
?? z[x]/x^3-1 # (z X z X z)
?? z[x]/x^3+x # (z X z X z) ...... ???? .... hmmmmm ..... ????? ......
??? f_q as algebraic ring here ??? .... ??? free algebraic module of algebraic ring on algebraic set ??? .... ???? ....
??? possibility of "twisted" version of "f_q as algebraic ring" here ??? .... ???? .... ?? maybe many such ??? .... ??? abelian variety p-torsion .... ???? ..... ??? "complex multiplication" ????? ..... ????? .....
?? f_p^n .... ??? ....
?? algebraic ring "the ring" ..... ??? .... polynomials in one variable ..... ????? ....... ?????? ...... ??? dirichlet polynomial ...... ?????? ...... ?? co-ring .... ???? ....
?? homming irreducible tensor factor stable hopf algs here into finite fields and / or finite semi-simple comm rings .... ??? ..... ????? ..... ???? add / mult confusion ..... ????? ..... ????? .....
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