The finite-degree profile of essential dimension I: general theory and characteristic prime to $|G|$ TPA3E67MKK
| URI | m2://res/TPA3E67MKK |
|---|---|
| Kind | preprint |
| Creators | Abhishek Shukla |
| Date | 2026-10-05 |
| MSC | 14-XX |
| Subjects | arxiv math.AG |
| Scope | in |
Expressions
e1: version, preprint
| Language | en |
|---|---|
| Date | 2026-10-05 |
| Ids | arXiv 2610.07508 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| shape | statement | proposition 3.2 | arxiv |
| 1NHBKZ41VN | statement | proposition 9.11 | arxiv |
| subgroup profile | statement | corollary 3.7 | arxiv |
| 2V74361HXN | problem | problem 10.3 | arxiv |
| 4BG7HNRVJW | statement | proposition 9.7 | arxiv |
| compositum degree | statement | lemma 7.2 | arxiv |
| profile of abelian groups | statement | corollary 7.10 | arxiv |
| the profile of $A_5$ | statement | corollary 9.12 | arxiv |
| a valuation with algebraically closed residue field and $A$ in the decomposition group | statement | lemma 7.3 | arxiv |
| 98JWVQA27K | statement | corollary 9.9 | arxiv |
| geometric meaning of the profile | statement | theorem 4.1 | arxiv |
| A3YRCPR4YM | statement | lemma 2.2 | arxiv |
| base-field extension bound | statement | proposition 3.8 | arxiv |
| A84PD538A5 | statement | fact 2.1 | arxiv |
| the generic torsor dominates every profile | statement | proposition 4.3 | arxiv |
| elementary abelian groups | statement | corollary 7.11 | arxiv |
| index of $\Gam_{F'}$ | statement | lemma 7.1 | arxiv |
| Rank--index bound | statement | theorem 7.6 | arxiv |
| DT1RXZ44RV | example | example 3.11 | arxiv |
| DWTYK1N9QC | problem | problem 10.4 | arxiv |
| DX890FWB5K | statement | lemma 9.8 | arxiv |
| Kummer | statement | lemma 7.9 | arxiv |
| FFEA1Z9PWB | statement | theorem A | arxiv |
| the per-torsor bound | statement | corollary 8.4 | arxiv |
| free points | statement | lemma 9.5 | arxiv |
| the last jump | statement | lemma 9.4 | arxiv |
| faithful $S_5$-curves | statement | lemma 9.6 | arxiv |
| tame structure | statement | lemma 7.4 | arxiv |
| prime-to-$q$ extensions of the base field | statement | lemma 5.2 | arxiv |
| consistency with equality | example | example 5.12 | arxiv |
| HWGF4NK0QY | definition | definition 3.1 | arxiv |
| Abhyankar's inequality | statement | lemma 7.5 | arxiv |
| J9E0DCQV14 | statement | lemma 8.1 | arxiv |
| JE1Z90NZRZ | statement | theorem 9.1 | arxiv |
| JKSZ9AZR7N | statement | theorem C | arxiv |
| KKXADGDXNN | statement | corollary 8.5 | arxiv |
| Sylow divisibility | statement | theorem 5.4 | arxiv |
| Karpenko--Merkurjev | statement | theorem 5.8 | arxiv |
| induced torsors | statement | lemma 3.6 | arxiv |
| roots-of-unity defect | statement | corollary 3.9 | arxiv |
| PHDHVR8B37 | statement | proposition 7.7 | arxiv |
| subgroup bound | statement | proposition 5.11 | arxiv |
| PQXH7FHT4E | statement | theorem B | arxiv |
| the witness curve | statement | proposition 6.4 | arxiv |
| compression | statement | lemma 6.2 | arxiv |
| the Karpenko--Merkurjev plateau | statement | proposition 5.9 | arxiv |
| purely inseparable invariance | statement | lemma 3.5 | arxiv |
| the first jump degree of $\Z/p$ | statement | theorem 8.2 | arxiv |
| purely transcendental base change | statement | lemma 6.1 | arxiv |
| base change to $\bar k$ | statement | lemma 9.3 | arxiv |
| V0JZJ1MBSR | problem | problem 8.6 | arxiv |
| V36TBFAKCW | statement | proposition 9.14 | arxiv |
| $K$ is regular over $k$; base change of $\tgen$ | statement | lemma 5.6 | arxiv |
| the subgroup formula for abelian groups | statement | corollary 7.13 | arxiv |
| the last jump degree | statement | proposition 3.3 | arxiv |
| W53B7GMJ4G | statement | proposition 5.3 | arxiv |
| Abel--Jacobi | statement | lemma 6.3 | arxiv |
| XFJ62G83CC | problem | problem 10.2 | arxiv |
| XWFRADVGQW | problem | problem 10.1 | arxiv |
| symmetric groups | example | example 9.15 | arxiv |
| ZM59HK3JTQ | statement | lemma 8.3 | arxiv |
| $q$-closure | statement | lemma 5.1 | arxiv |
| $q$-groups | statement | proposition 5.7 | arxiv |
Catalogue records
- arxiv: 2610.07508 (work)
- arxiv_text: 2610.07508 (work)