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Record W1968778786 · doi:10.1155/imrn/2006/53864

Evil primes and superspecial moduli

2006· article· en· W1968778786 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueInternational Mathematics Research Notices · 2006
Typearticle
Languageen
FieldMathematics
TopicAdvanced Mathematical Identities
Canadian institutionsMcGill University
Fundersnot available
KeywordsMathematicsModuliPure mathematicsPhysics

Abstract

fetched live from OpenAlex

For a quartic non-biquadratic CM field K, we say that a rational prime p is evil forK if at least one of the principally polarized abelian varieties with CM by K reduces modulo a prime ideal p|p to a product of supersingular elliptic curves with the product polarization. We showed that for fixed K, such primes are bounded by a quantity related to the discriminant of K. We show that evil primes are ubiquitous in the sense that for any rational prime p, there are an infinite number of such CM fields K for which p is evil. (Assuming a standard conjecture, the result holds for a finite set of primes simultaneously.) The proof consists of two parts: (1) showing the surjectivity of the principally polarized abelian varieties with CM by K, for K satisfying some conditions, onto the superspecial points of the reduction modulo p of the Hilbert modular variety associated to the intermediate real quadratic field of K, and (2) showing the surjectivity of the superspecial points of the reduction modulo p of the Hilbert modular variety associated to a real quadratic field with large enough discriminant onto the superspecial points on the reduction modulo p of the Siegel moduli space parameterizing abelian surfaces with principal polarization.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.297
Threshold uncertainty score0.777

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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.

Opus teacher head0.156
GPT teacher head0.461
Teacher spread0.305 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it