Lower bounds for the number of semidualizing complexes over a local ring - Sather-Wagstaff, Sean (MATHEMATICA SCANDINAVICA, 2012)
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 2^n 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 2^n, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism φR→ 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).