2001
DOI: 10.1007/pl00000510
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Quasi-polynomials associated with Bass and Betti numbers of filtered modules

Abstract: It is shown that if M is a finite module on a local noetherian ring A which is filtered by an f -good filtration Φ = (M n ) where f is a noetherian filtration on A, then the i-th Betti and the i-th Bass numbers of the modules (M n ) and (M/M n ) define quasipolynomial functions whose period does not depend on i but only of the Rees ring of f . It is proved that the projective and injective dimension of the modules M/M n are perodic for large n. In the particular case where f is a good filtration or a strongly … Show more

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