?? conventional-geometric interpretation of toric quasicoherent sheaf ...

?? what's special about spectrum of a permutation matrix ?? .... ?? "subgroup-like" ??? ....

?? relationship to constraining loop periodicity / tail length ?? .... ???? ...

?? fan geometry here ?? ....

?? coalgebra / coalgebra .... ????? ....

??toric divisor ... ??? ...

?? recovering arbitrary quasicoherent sheaf as ab gp toric quasicoherent sheaf .... ??? ....