?? using lagrange extrapolation to construct alg ab gp structure on spec(xXz) for x quadratic number ring ..... .... .... ??? ...

?? exponentiableness and "flatness" ??? ... affine line ^ spec(r) .... ??? to what extent this gives good "algebraic model" of r ... ???? ..... ?? exponentiableness and geometric colimits (= algebraic limits ...) ... preservation of them by cartesian (tensor ...) product with exponent e .... ?? modification of colimits and getting more objects to be exponentiable .... ???? ...

?? power series ring .... ??? ....


?? doctrine in which concept "field" can be nicely expressed .... ???? ......

?? tag (??) theory for d-building .... ???? ....

?? spec(gaussian integers) as exponent ... ??? "for each original generator g, generators g_1 and g_i ... for each original relator r, relators r_1 and r_i ..." ...

?? bit about "underlying real variety of complex variety" .... ?????? ....

?? walking idempotent ... r = [gg=g] ... g_1=h, g_r=j ... (h+ji)(h+ji)=h+ji ...

hh-jj = h

jh+hj = j

????

?? measure vs function .... ????? .....

2hj = j

2hj-j = 0

(2h-1)j = 0 ...

?? .... 1/4 - jj = 1/2

jj - 1/4 = -1/2

jj = 1/4 - 1/2

jj = -1/4 ....

j =?= plus or minus i/2

?? h+ji = 1/2 + (i/2)i = 0 .....

?? what in the world is going on here ???? .....

?? spec(r^2) ^ spec(c) ..... ????? ?? over r ..... ????? .....

?? alg ab gp vs motive .... ???? .... ?? ab cat of alg ab gps ?? ... ???? ...

??? "imaginary numbers drag real numbers down so complex field has no real spectrum" .... ???? ....

?? some algebra/geometry contravariance confusion here, but ... ???? ...

?? mystical arrow / dominance / superscript confusion ??? ..... ....

hh-jj = h

2hj = j

(2h-1)j = 0

?? "h = 1/2 or [j=0 and consequently hh=h]" .... ????? ...

?? components of the exponential here ... ?? "real" vs ... ?? "unreal" (????) such .... ???? ...... actual morphism ... "occupied" .... ??? .... ???? ....

?? relationship to exponentiation in group action topos ?? ... ?? "preservation of exponentiation by forgetful functor" .... ???? ....

?? (1+1)^2 = 1+2+1 ..... ????? ....