??mapping from spec(finite comm ring) to exponential spec(z^n)^[number ring] .... ????

spec(finite comm ring) X [number ring] -> spec(z^n) .... ??? ....

?? number of components that number ring splits into when tensored with finite comm ring .... ????? .....

?? for example number ring = gaussian integers ... ?? .... ?? and n = 3, say ... ?? ...

?? finite comm rings of size one ... ?? ....

?? zero components ??? ... ?? one map ?? ....

?? size two ?? ...

?? is it just one component ?? ... ??? because of ramification ??? ... so 3 maps ?? ....

?? size three ... ??? ...

?? one component .... ?? so 3 maps ??? .....

?? size 4 .... ??? 2 iso classes of semi-simple comm rings here .... ??? ... f_4 and f_2 X f_2 .... ???? .....

?? ...