?? (?? affine ?? ...) algebraic ring whose underlying scheme is exponentiable (?? in "affine" sense ??? .... ???? ....)

?? affine algebraic ring like "the gaussian integers" .... ????? .... role of "flatness" (??? ... ????) of k in making functor _comm ring_ -> _comm ring_ -> _set_ given by [tensoring with k] followed by "underlying set" sufficiently good (=?= representable ... ??? ....) ... ????? .... ???? ....

?? "algebraic integers" here as trickier but maybe interesting ... ??? ... ?? not affine but ... ??? ....

?? had ideas about using this (...) sort of algebraic ring stuff to get nice twisted versions of finitary bistable hopf algs (and "distributive" such ...... ???? .....) ..... ??? not quite sure about that idea now ??? .... ????? ...... ?? level slip ??? .... coefficients vs .... ??? .... ??? .... ???????? "splitting" ...... ???? "trivial" .... ?? "locally trivial" .... ????? "flat" ????? ..... ????? ......

?? alg ideal in alg ring ... modding out by such .... ??? .... ??? ....

??? alg rep of alg gp .... ???? .... ?? alg hom to alg matrix (?? ...) ring ... ???? ....

??? vague memory about ... ?? "geometric (?? ....) version of frobenius ..." .... ???? categorified zeta function .... ????? .... ??? ....

rig .... ??? comm rig as between comm monoid and comm ring ... of course other things in between there too ... ???? ....

??? divisor concept on "reducible" variety ... ??? use product of meromorphic fields here ..... ????? .....