On unipotent radicals of motivic Galois groups
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.
Bibliographic record
Abstract
Let T be a neutral Tannakian category over a field of characteristic zero with unit object 1, and equipped with a filtration W • similar to the weight filtration on mixed motives.Let M be an object of T , and u(M) ⊂ W -1 Hom(M, M) the Lie algebra of the kernel of the natural surjection from the fundamental group of M to the fundamental group of Gr W M. A result of Deligne gives a characterization of u(M) in terms of the extensions 0 → W p M → M → M/W p M → 0: it states that u(M) is the smallest subobject of W -1 Hom(M, M) such that the sum of the aforementioned extensions, considered as extensions of 1 by W -1 Hom(M, M), is the pushforward of an extension of 1 by u(M).We study each of the abovementioned extensions individually in relation to u(M).Among other things, we obtain a refinement of Deligne's result, where we give a sufficient condition for when an individual extension 0 → W p M → M → M/W p M → 0 is the pushforward of an extension of 1 by u(M).In the second half of the paper, we give an application to mixed motives whose unipotent radical of the motivic Galois group is as large as possible (i.e., with u(M) = W -1 Hom(M, M)).Using Grothendieck's formalism of extensions panachées we prove a classification result for such motives.Specializing to the category of mixed Tate motives we obtain a classification result for 3-dimensional mixed Tate motives over ޑ with three weights and large unipotent radicals.
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 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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.016 | 0.005 |
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