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In abstract algebra (specifically commutative ring theory), Faltings' annihilator theorem states: given a finitely generated module M over a Noetherian commutative ring A and ideals I, J, the following are equivalent: * for any , * there is an ideal in A such that and annihilates the local cohomologies , provided either A has a dualizing complex or is a quotient of a regular ring. The theorem was first proved by Faltings in.
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