Lower bounds for the number of semidualizing complexes over a local ring

Authors

  • Sean Sather-Wagstaff

DOI:

https://doi.org/10.7146/math.scand.a-15192

Abstract

We investigate the set $\mathfrak(R)$ 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 $\mathfrak(R)$ has cardinality $2^n$ for some $n$. We show that, if there is a chain of length $n$ in $\mathfrak(R)$ and if the reflexivity ordering on $\mathfrak (R)$ is transitive, then $\mathfrak(R)$ has cardinality at least $2^n$, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism $\varphi\colon R\to S$ of finite flat dimension, if $R$ and $S$ admit dualizing complexes and if $\varphi$ is not Gorenstein, then the cardinality of $\mathfrak (S)$ is at least twice the cardinality of $\mathfrak (R)$.

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Published

2012-03-01

How to Cite

Sather-Wagstaff, S. (2012). Lower bounds for the number of semidualizing complexes over a local ring. MATHEMATICA SCANDINAVICA, 110(1), 5–17. https://doi.org/10.7146/math.scand.a-15192

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Section

Articles