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Non-commutative Castelnuovo-Mumford regularity

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

We define Castelnuovo–Mumford regularity for graded modules over non-commutative graded algebras. Two fundamental commutative results are generalized to the non-commmutative case: a vanishing-theorem by Mumford, and a theorem on linear resolutions and syzygies by Eisenbud and Goto. The generalizations deal with sufficiently well-behaved algebras (i.e. so-called quantum polynomial algebras). We go on to define Castelnuovo–Mumford regularity for sheaves on a non-commutative projective scheme, as defined by Artin. Again, a version of Mumford's vanishing-theorem is proved, and we use it to generalize a result by Martin, Migliore and Nollet, on degrees of generators of graded saturated ideals in polynomial algebras, to quantum polynomial algebras. Finally, we generalize a practical result of Schenzel which determines the regularity of a module in terms of certain Tor-modules.


Publication metadata

Author(s): Jørgensen P

Publication type: Article

Publication status: Published

Journal: Mathematical Proceedings of the Cambridge Philosophical Society

Year: 1999

Volume: 125

Issue: 2

Pages: 203-221

Print publication date: 01/01/1999

Publisher: Cambridge Philosophical Society

URL: http://journals.cambridge.org/abstract_S0305004198002862


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