3 problems

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Quillen's finite-flat-dimension conjecture for the cotangent complex
Quillen's conjecture. If $\operatorname{L}(\varphi)$ has finite flat dimension, then $\varphi$ is locally complete intersection.
Theoremopencommutative-algebra complete-intersections cotangent-complexarXiv posted 2 days ago
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Vasconcelos's cotangent-module conjecture in characteristic zero
Vasconcelos's conjecture. If $\Omega_{S/R}$ has finite projective dimension over $S$ , then $S$ is a locally complete intersection ring.
Conjectureopencommutative-algebra complete-intersections cotangent-complexarXiv posted 2 days ago
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Herzog's cotangent homology conjecture
Herzog's cotangent homology conjecture. The following conditions are equivalent:
Conjectureopencommutative-algebra complete-intersections cotangent-complexarXiv posted 2 days ago

Quillen's finite-flat-dimension conjecture for the cotangent complex