Variations of Demushkin Groups that are not Absolute Galois Groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915905015906304 |
|---|---|
| author | Blumer, Simone Quadrelli, Claudio |
| author_facet | Blumer, Simone Quadrelli, Claudio |
| contents | We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new examples of pro-p groups that do not occur as maximal pro-p Galois groups of fields containing a root of unity of order p - and thus, as absolute Galois groups. Moreover, we show that these pro-p groups may not be ruled out as maximal pro-p Galois groups employing other cohomological properties that are known to hold for all maximal pro-p Galois groups, such as the triple Massey vanishing property, or the quadraticity of Fp-cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variations of Demushkin Groups that are not Absolute Galois Groups Blumer, Simone Quadrelli, Claudio Group Theory K-Theory and Homology Primary 12G05, Secondary 20E18, 20J06, 12F10, 17B70, 17B56 We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new examples of pro-p groups that do not occur as maximal pro-p Galois groups of fields containing a root of unity of order p - and thus, as absolute Galois groups. Moreover, we show that these pro-p groups may not be ruled out as maximal pro-p Galois groups employing other cohomological properties that are known to hold for all maximal pro-p Galois groups, such as the triple Massey vanishing property, or the quadraticity of Fp-cohomology. |
| title | Variations of Demushkin Groups that are not Absolute Galois Groups |
| topic | Group Theory K-Theory and Homology Primary 12G05, Secondary 20E18, 20J06, 12F10, 17B70, 17B56 |
| url | https://arxiv.org/abs/2603.15464 |