A freeness criterion for complexes with derived actions
Sylvain Brochard, Srikanth B. Iyengar, and Chandrashekhar B. Khare
TL;DR
This paper proposes a new conjectural criterion for determining when complexes over certain rings are free, inspired by patching methods and verified in specific cases, advancing understanding in algebraic structures.
Contribution
It introduces a conjectural freeness criterion for complexes with derived actions, avoiding patching, and confirms its validity in multiple instances.
Findings
Proposes a conjectural freeness criterion for complexes over noetherian local rings.
Verifies the criterion in several specific cases.
Provides insights inspired by patching methods and a proven conjecture.
Abstract
Inspired by the patching method of Calegari and Geraghty, and a conjecture of de Smit that has been proved by the first author, we present a conjectural freeness criterion without patching for complexes over commutative noetherian local rings with derived actions, and verify it in several cases.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology