Abstract
One can associate to each finitely presented module M over a commutative ring R an R -ideal Fitt R ( M ) which is called the (zeroth) Fitting ideal of M over R and which is an important natural invariant of M . We generalize this notion to o -orders in separable algebras, where o is a complete commutative noetherian local ring. As an application we construct annihilators of class groups assuming the validity of the Equivariant Tamagawa Number Conjecture for a certain motive attached to a Galois CM-extension of number fields.
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