Chasing Maximal Pro-p Galois Groups via 1-Cyclotomicity
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Bibliographic record
Abstract
Abstract Let p be a prime. We prove that certain amalgamated free pro- p products of Demushkin groups with pro- p -cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro- p group, and thus do not occur as maximal pro- p Galois groups of fields containing a root of 1 of order p . We show that other cohomological obstructions which are used to detect pro- p groups that are not maximal pro- p Galois groups—the quadraticity of $$\mathbb {Z}/p\mathbb {Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>p</mml:mi> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> -cohomology and the vanishing of Massey products—fail with the above pro- p groups. Finally, we prove that the Minač–Tân pro- p group cannot give rise to a 1-cyclotomic oriented pro- p group, and we conjecture that every 1-cyclotomic oriented pro- p group satisfy the strong n -Massey vanishing property for $$n=3,4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> .
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it