<i>p</i>-adic <i>L</i>-functions and the coniveau filtration on Chow groups
Bibliographic record
Abstract
Abstract We give evidence for the refined version of the Beilinson–Bloch conjecture involving coniveau filtrations, by studying several infinite families of CM motives (indexed by the integers <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>r</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {r\geq 1} ) that are irreducible of Hodge type <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>r</m:mi> </m:mrow> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>,</m:mo> <m:mn>0</m:mn> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mrow> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>r</m:mi> </m:mrow> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> {(2r+1,0)+(0,2r+1)} and whose L -functions vanish at the center. In each case, we construct a corresponding algebraic cycle that is homologically trivial but nontrivial in the top graded piece for the coniveau filtration. Consequently, we obtain new explicit examples of cycles on varieties over number fields that are nontorsion in the Griffiths group. The proof of the main result relies crucially on p -adic Hodge theoretic methods, and in particular on the relation between images of homologically trivial cycles under the p -adic Abel–Jacobi map and the values of p -adic L -functions.
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How this classification was reachedexpand
Full frame distilled prediction
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 | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".