?? equivalence of categories between .... ??? invertible (?? as more than just property ?? ... ??? ..... hmm, i seem to be "going beyond gpd regime" here ... ??? ....) modules of z/n, and "n-cyclotomic fields" ??? .... ?? given in reverse direction by taking the nth roots of unity, with their multiplication structure ... as the addition in the invertible module ... ??? ....

?? generalize .... ??? .... understand .... ??? ....