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Maximal Cohen-Macaulay Complexes and Their Uses: A Partial Survey

In: Commutative Algebra

Author

Listed:
  • Srikanth B. Iyengar

    (University of Utah, Department of Mathematics)

  • Linquan Ma

    (Purdue University, Department of Mathematics)

  • Karl Schwede

    (University of Utah, Department of Mathematics)

  • Mark E. Walker

    (University of Nebraska, Department of Mathematics)

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.

Suggested Citation

  • Srikanth B. Iyengar & Linquan Ma & Karl Schwede & Mark E. Walker, 2021. "Maximal Cohen-Macaulay Complexes and Their Uses: A Partial Survey," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, pages 475-500, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-89694-2_15
    DOI: 10.1007/978-3-030-89694-2_15
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