Relative Trace Ideals and Cohen - Macaulay Quotients of Modular Invariant Rings
نویسنده
چکیده
Let G be a nite group, F a eld whose characteristic p divides the order of G and A G the invariant ring of a nite-dimensional FG-module V. In analogy to modular representation theory we deene for any subgroup H G the (relative) trace-ideal A G H /A G to be the image of the relative trace map t G X is always a proper ideal of A G ; in fact, we show that its height is bounded above by the codimension of the xed point space V P. But we also prove that if V is relatively X-projective, then A G X still contains all invariants of degree not divisible by p. If V is projective then this result applies in particular to the (absolute) trace ideal A G feg. We also give a `geometric analysis' of trace ideals, in particular of the ideal A G <P :=
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