MathDBQ-sequence conjecture for systems of parameters
Q-sequence conjecture for systems of parameters
Let be a Noetherian local ring of dimension . A sequence is a system of parameters when it generates an ideal whose radical is the maximal ideal; more generally, in the nonlocal formulation, let be a Noetherian ring and let be a sequence such that has a minimal prime of height . Q-sequence conjecture. Every system of parameters for is a Q-sequence. More generally, under the stated nonlocal hypotheses, is a Q-sequence. The paper has established the equicharacteristic Noetherian local case and gives related sufficient conditions, but does not state a resolution of this broader conjecture.
Equivalent formulations 1
Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.
The Q-sequence conjecture for systems of parameters
Let be a local ring, and let be a system of parameters. A Q-sequence is a sequence with the quasilength property used in the definition of robust algebras. Q-sequence conjecture. Every system of parameters for every local ring is a Q-sequence. Hence, every Noetherian ring is robust as an algebra over itself. This would characterize robustness of Noetherian rings over themselves through systems of parameters, extending the role of Q-sequences in the theory of solid and robust algebras. The supplied text gives no resolution status.
source: Mel Hochster and Wenliang Zhang, “Content of Local Cohomology, Parameter Ideals, and Robust Algebras”, arXiv:1609.07017 (2016).
Sources & referencesView supporting material
Primary source
Olivia Strahan, “Content and Q-sequences in Mixed Characteristic Local Rings”, arXiv:2310.19937 (2024).
Progress summary
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