Rouquier dimension versus global dimension
Greg Stevenson
TL;DR
This paper presents an example of a commutative coherent ring with infinite global dimension but finite Rouquier dimension of its perfect complexes, challenging previous assumptions about their relationship.
Contribution
It provides a counterexample showing that finite Rouquier dimension does not imply finite global dimension in commutative rings.
Findings
Counterexample with infinite global dimension and finite Rouquier dimension
Challenging assumptions about the relationship between global and Rouquier dimensions
Insights into the structure of perfect complexes in commutative rings
Abstract
We give an example of a commutative coherent ring of infinite global dimension such that the category of perfect complexes has finite Rouquier dimension.
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Taxonomy
TopicsAdvanced Topics in Algebra · Optimization and Variational Analysis · Advanced Optimization Algorithms Research