Bibliographic record
Abstract
In this thesis we study moduli stacks \\calM_\\Phi^n, indexed by an integer n>0 and a CM-type (K,\\Phi), which parametrize abelian schemes equipped with action by \\OK and an \\OK-linear principal polarization, such that the representation of \\OK on the relative Lie algebra of the abelian scheme consists of n copies of each character in \\Phi. We do this by systematically applying Serre's tensor construction, and for that we first establish a general correspondence between polarizations on abelian schemes M\\otimes_R A arising from this construction and polarizations on the abelian scheme A, along with positive definite hermitian forms on the module M. Next we describe a tensor product of categories and apply it to the category \\Herm_n(\\OK) of finite non-degenerate positive-definite \\OK-hermitian modules of rank n and the category fibred in groupoids \\calM_\\Phi^1 of principally polarized CM abelian schemes. Assuming n is prime to the class number of K, we show that Serre's tensor construction provides an identification of this tensor product with a substack of the moduli space \\calM_\\Phi^n, and that in some cases, such as when the base is finite type over \\CC or an algebraically closed field of characteristic zero, this substack is the entire space. We then use this characterization to describe the Galois action on \\calM_\\Phi^n(\\overline{\\QQ}), by using the description of the action on \\calM_\\Phi^1(\\overline{\\QQ}) supplied by the main theorem of complex multiplication.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".