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

2021/06/15 by Srikanth B. Iyengar, Linquan Ma, Iyengar, Srikanth B. +5 · 2 citations
Mathematics · #13D02 (primary) #13D22 #13D45 #14E15 #14F18 (secondary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2106.08173

openalex publication_date 2021/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 André. 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.

Cited by

• A lower bound on levels with applications to Koszul Complexes
• On the depth of tensor products over Cohen-Macaulay rings

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• Maximal Cohen-Macaulay DG-Complexes
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