Lower bounds for the number of semidualizing complexes over a local ring
- Autores: Sean Sather-Wagstaff
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 1, 2012, págs. 5-17
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15192
- Enlaces
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Resumen
We investigate the set (R) of shift-isomorphism classes of semi-dualizing R-complexes, ordered via the reflexivity relation, where R is a commutative noetherian local ring. Specifically, we study the question of whether (R) has cardinality 2n for some n. We show that, if there is a chain of length n in (R) and if the reflexivity ordering on (R) is transitive, then (R) has cardinality at least 2n, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism φ:R→S of finite flat dimension, if R and S admit dualizing complexes and if φ is not Gorenstein, then the cardinality of (S) is at least twice the cardinality of (R).
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