?? bit about something like galois rep arising from stable hopf alg ... ?? stable hopf alg here as morally "affine algebraic abelian group" ??? .... ???? ....

"algebraic k-module" .... ?? possibility of k being external constant, or itself an algebraic comm ring ...... ????? such as "_the_ comm ring" ..... ????

?? example of algebraic module over algebraic comm ring "the comm ring" ... ???? ....

?? "the comm ring" ... ??? affine algebraic comm ring ... spec(k[x]) .... ?? affine algebraic module over it ???? .....

?? spec(k[x,y]) as another affine algebraic comm ring ... ?? in fact affine algebraic comm alg over the previous one .... ??? .... ?? with the comultiplication (x |-> x1*x2, y |-> y1*x2 + y2*x1) ...... ?????? ....

?? vague memory of ... ??? slightly exotic hopf alg (?? ...) example we thought about ... ?? and coincidentally read someone else write something about .... ?? galois flavor .... ??? ....

?? "finite" sub-[algebraic group] of gl(1) or of some particular abelian variety, for example .... ??? ....

gl(1) as affine algebraic ... spec(k[x,y]/xy-1) .... spec(k[x]/x^n-1) ... ?? as obtained by modding out by (?? "hopf" ??? ... ???? ....) ideal ... ?? ....

?? affine algebraic subgp of non-affine algebraic gp .... ???? .....

?? hopf alg arising as gp alg ... of external constant gp ..... ??? .... ?? fourier duality confusion here ???? ..... ???? ....

???? algebraic fourier dual of external constant gp as not external constant ??? ..... ???? .....

?? k[x]/x^2-1 vs k^2 ???? .... ?? well, maybe in that particular case there's no difference .... ??? but try .... ????? k[x]/x^3-1 vs k^3 .... ???? ...... whether these are "algebraic fourier dual" ??? .... ?? that is, measures on z/3 vs functions on z/3 .... ??? z-valued ???? .... ?? evaluation (??? .... or maybe "integration" more apt terminology here ??? .... ??? ......) pairing .... ???

?? "split" ... ?? ....

??? "algebraic (?? "fourier" ??? ....) dual" of finite affine sub-gp of abelian variety ???? ....... ????? ....... ?????? ......

??? "applying any functor to k-bar as giving action of abs galois gp of k" .... ????? .....

?? functions : external constant :: measures : twisted ...... ????? ..... ??? in "external constant" case ??? ..... ?????? ......