English

Maximal Cohen-Macaulay complexes and their uses: A partial survey

Commutative Algebra 2021-06-16 v1

Abstract

This work introduces a notion of complexes of maximal depth, and maximal Cohen-Macaulay complexes, over a commutative noetherian local ring. The existence of such complexes is closely tied to the Hochster's ``homological conjectures", most of which were recently settled by Andr\'e. Various constructions of maximal Cohen-Macaulay complexes are described, and their existence is applied to give new proofs of some of the homological conjectures, and also of certain results in birational geometry.

Keywords

Cite

@article{arxiv.2106.08173,
  title  = {Maximal Cohen-Macaulay complexes and their uses: A partial survey},
  author = {Srikanth B. Iyengar and Linquan Ma and Karl Schwede and Mark E. Walker},
  journal= {arXiv preprint arXiv:2106.08173},
  year   = {2021}
}

Comments

20 pages

R2 v1 2026-06-24T03:13:31.551Z