O-minimal spectra, infinitesimal subgroups and cohomology
| dc.creator | Berarducci, Alessandro | |
| dc.date | 2006-04-09 | |
| dc.date.accessioned | 2026-07-07T07:10:40Z | |
| dc.date.available | 2026-07-07T07:10:40Z | |
| dc.description | By recent work on some conjectures of Pillay, each definably compact group $G$ in a saturated o-minimal expansion of an ordered field has a normal ``infinitesimal subgroup'' $G^{00}$ such that the quotient $G/G^{00}$, equipped with the ``logic topology'', is a compact (real) Lie group. Our first result is that the functor $G\mapsto G/G^{00}$ sends exact sequences of definably compact groups into exacts sequences of Lie groups. We then study the connections between the Lie group $G/G^{00}$ and the o-minimal spectrum $\widetilde G$ of $G$. We prove that $G/G^{00}$ is a topological quotient of $\widetilde G$. We thus obtain a natural homomorphism $Ψ^*$ from the cohomology of $G/G^{00}$ to the (Čech-)cohomology of $\widetilde G$. We show that if $G^{00}$ satisfies a suitable contractibility conjecture then $\widetilde {G^{00}}$ is acyclic in Čech cohomology and $Ψ^*$ is an isomorphism. Finally we prove the conjecture in some special cases. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604186 | |
| dc.identifier | http://arxiv.org/abs/math/0604186 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111490 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.subject | 03C64, 22E15, 03H05 | |
| dc.title | O-minimal spectra, infinitesimal subgroups and cohomology | |
| dc.type | text |