Class Groups of Multiplicative Invariants
نویسنده
چکیده
Let G be a nite subgroup of GL d (Z). Then G acts on the Laurent polynomial ring kX 1 1 d ] over the eld k via the natural G-action on the multiplicative group generated by the variables X 1 ; : : : ; X d (= Z d). We show that the class group of the ring of invariants of this action is isomorphic to Hom(G=N;k) H 1 (G=D; (Z d) D), where N denotes the subgroup of G that is generated by all reeections in G and D the subgroup generated by the reeections that are diagonalizable over Z.
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