Finite central extensions of o-minimal groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908284627189760 |
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| author | Baro, Elías Palacín, Daniel |
| author_facet | Baro, Elías Palacín, Daniel |
| contents | We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \cite{BPP10} for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \cite{jM83}. We prove that every abstract finite central extension of a definably connected solvable definable group in an o-minimal structure is equivalent to a definable (hence topological) finite central extension. The proof relies on an o-minimal adaptation of the higher inflation-restriction exact sequence due to Hochschild and Serre. As in \cite{jM83}, we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite central extensions of o-minimal groups Baro, Elías Palacín, Daniel Logic We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \cite{BPP10} for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \cite{jM83}. We prove that every abstract finite central extension of a definably connected solvable definable group in an o-minimal structure is equivalent to a definable (hence topological) finite central extension. The proof relies on an o-minimal adaptation of the higher inflation-restriction exact sequence due to Hochschild and Serre. As in \cite{jM83}, we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups. |
| title | Finite central extensions of o-minimal groups |
| topic | Logic |
| url | https://arxiv.org/abs/2407.16440 |