fan spectrum ....

flag variety ... subvariety ....

fan cone as toric orbit ,,,, ???? ....

?? "ghost point of cone" ... ??? .... (R,+)-spectrum vs (P,+)-spectrum .... ??? todd's subtlety and blow-up ????? ....

??? "available non-invertibles take over the role of zero" .... ???? .....

??? combinatorial ("schematic") aspect of fan as "2"-spectrum ... ??? comm monoid hom (P,+) -> 2 corresponding to mapping from "real" to "combinatorial" aspect of fan ... ???? other interesting homomorphisms here ??? .... ?? or non-homomorphisms or missing homomorphisms or something, to explain some of the weird stuff ??? .... ??? non-preservation of non-invertibility .... (?? somewhat dramatically so ??? .... "localization" .... ???? .....) ..... free (?? ... or ... ??? ....) boolean algebra .... ???? .... ??? also non-commutative diagram of homomorphisms ... ??? ....

?? does blow up map literally induce bijection on P-spectrum ???? .... ???? ....


???? hmmm .... ???? climbing from fan spectrum to whole real spectrum by ... inclusion (P,+) into (R,+), understood in terms of "ghost points" ... hopefully incorporating blow-up in a nice way .... .... ??? then .... (R,*) almost onto (R,+) ..... ????? ..... ??? .... ????? .....