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:Takesi Kawasaki, On Faltings' Annihilator Theorem, Proceedings of the American Mathematical Society, Vol. 136, No. 4 (Apr., 2008), pp. 1205–1211. NB: since , the statement here is the same as the one in the reference. for any prime ideal , 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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