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Ring Homomorphisms and Finite Gorenstein Dimension
Author(s) -
Avramov LL,
Foxby HB
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000348
Subject(s) - mathematics , homomorphism , dimension (graph theory) , pure mathematics , global dimension , ring (chemistry) , algebra over a field , organic chemistry , chemistry
The local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which substantially weakens the notion of finite flat dimension, is introduced for homomorphisms. It is shown to impose structural constraints, due to a remarkable equivalence of subcategories of the derived category of all modules. An essential part of this study is the development of relative notions of dualizing complexes and Bass numbers. It is proved that the Bass numbers of local homomorphisms are rigid, extending a known result for local rings. Quasi‐Gorenstein homomorphisms are introduced as local homomorphisms that base‐change a dualizing complex for the source ring into one for the target. They are shown to have the stability properties of the Gorenstein homomorphism that they generalize. 1991 Mathematics Subject Classification : primary 13H10, 13D23, 14E40; secondary 13C15.