?? role of zero in "toric birational geometry" ... ??? .... homomorphism into "toric field" taking zero as value .... ???? .....

??? "place of toric field" ... ??? ..... "archimedeanness" and/or other types of non-/pathology ... ????? ....

??? underlying TAG theory of AG theory of r-modules, vs TAG theory of [underlying monoid](r)-actions, for comm rig r .... ????? .... ??? ..... spectrums ... ??? ..... wrt such various things ... ??? ... ???? .....