Faltings’ Finiteness Dimension of Local Cohomology Modules Over Local Cohen–Macaulay Rings
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Bibliographic record
Abstract
Abstract Let ( R , m ) denote a local Cohen–Macaulay ring and I a non-nilpotent ideal of R . The purpose of this article is to investigate Faltings’ finiteness dimension f I ( R ) and the equidimensionalness of certain homomorphic images of R . As a consequence we deduce that f I ( R ) = max{1, ht I }, and if mAss R ( R/I ) is contained in Ass R ( R ), then the ring is equidimensional of dimension dim R −1. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module , in the case where ( R ,m) is a complete equidimensional local ring.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it