?? functor assigining to finite field x(?? or semi-simple comm ring ?? ... ???? ..... ??? ....) f_p-vsp (... ?? ... of pth roots of unity in x) ... ?????? ......
?? proof of cyclicness of finite (?? ...) subgp of mult gp of field .. ??? otherwise impossibly many nth roots of unity for some n ??? ... ???? ... ??? .... ?? generalizations ..... ???? .... ???? from 1d vsp to higher-dim ??? ... ????? ... ??? ....
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