?? gaussian integers .... homming into finite semi-simple comm ring .... ?? ....

0

1 1 - 1 1

2 f_2 1 1 1

3 0

4 f_2 X f_2 1,1 2 f_4 1 2 1

5 f_5 2 1 3 1 2

6 0

7 0

8 f_2 X f_2 X f_2 1,1,1 6 f_2 X f_4 1,1 2 f_8 1 3 1

??? counting points of spectrum of alg comm ring over finite fields .... ??? ...

_comm ring_ -> _comm ring_ .... ???? ... "tensoring with gaussian integers" ....

?? confusion ?? ... ?? level slip ??? .... ??? pretty big algebraic comm ring ... ??? polynomials in 2 variables .... inf-dim ... ??? vs pretty small hopf algs .... ???? .... ??? .... fin-dim .... ???? ...

?? 4th roots of 1 mod square roots of 1 ??? ..... ???? ....

?? 3rd roots of 1 ........ ?????? .....