A local ring has only finitely many semidualizing complexes up to shift-isomorphism

Details A local ring has only finitely many semidualizing complexes up to shift-isomorphism A local ring has only finitely many semidualizing complexes up to shift-isomorphism

2011-12-29

arxiv.org/abs/1201.0037v2

Mathematics

Commutative Algebra

31 pages, v.2 has minor corrections and updated references

Scientific paper

A homologically finite complex C over a commutative noetherian ring R is "semidualizing" if RHom_R(C,C) \simeq R in D(R). We answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many shift-isomorphism classes of semidualizing complexes. Our proof relies on certain aspects of deformation theory for DG modules over a finite dimensional DG algebra, which we develop.

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