= December 20 = So: I have been unable to find any proof for claims (1) and (2). (I don`t know if they are true or not, I conjectured them.) In particular, with (1), I don`t have a sufficiently explicit form for the Artin map to even attempt a proof. As for (3), I don`t really have any ideas. Would anybody be able to give any guidance with thes......