Sunday, July 25, 2010

inertia subgroup and frobenius conjugacy class

trying to understand various ideas connected with this stuff...

suppose that we've got a gXh-set x....

and an elt x1 in x ....

and consider the "stabilizer in g of the h-orbit of x1" ... os....

??so... this stabilizer acts on the transitive h-set given by this h-orbit ... os....

and the aut gp of that h-orbit is the normalizer in h of the stabilizer in h of x1, modulo that stabilizer .... ???os???....

??but we're mainly interested in the case where h is abelian, so what seemed slightly interesting there mostly just degenerates??? os???.... meanwhile... ??what happens to make this "frobenius" stuff work??? os??? .....

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