?? so .... idea that difference in flavor between "(absolutely...) absolute" and "imaginary quadratic" cases of jugendtraum is because of always ramified at -1 vs never so .... ?? and that this in some way lets you get away with thinking purely in terms of multiplicative groups of quotient rings (?? ...) in imaginary quadratic case .... ??? .... ??? though also so in the absolutely absolute case, apparently, but for some presumably slightly different reason ??? ..... ???? ....

?? abelian extension vs radical extension .... visual intuition about "subdivision" here .... ??? ... threatening to make things _ridiculously_ simple ... ?? "the subfiled practically _is_ the subgroup" .... ??? ..... ?? but .... ??? ......

?? gaussian integers .... quartic reciprocity .... ??? .... also eisentstein and cubic .... ???? .... ?? "reciprocity" ..... ??????? .......

?? "theta constants" ...... ???? "hodge structure" .... ??? .... ???? ....

?? field generated by coordinates (?? ...) of all rational subdivision points of all algebraic groups .... ??? ..... ???? ..... ?? non-abelianness here ??? ....

?? "existentially closed groups" and "galois theory" ??? ..... ???? .... "algebriac closure" ... ??? ... ??? ....?? "duality" .... ???? .... ???? .....