An obstruction to the local lifting problem
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916752002121728 |
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| author | Kontogeorgis, Aristides Terezakis, Alexios |
| author_facet | Kontogeorgis, Aristides Terezakis, Alexios |
| contents | We are investigating the lifting problem for local actions involving semidirect products of a cyclic $p$-group with a cyclic group prime to $p$, where $p$ represents the characteristic of the special fiber. We establish a criterion based on the Harbater-Katz-Gabber compactification of local actions, enabling us to determine whether a given local action can be lifted or not. Specifically, in the case of the dihedral group, we present an example of a local dihedral action that cannot be lifted. This instance provides a more potent obstruction than the KGB obstruction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08377 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An obstruction to the local lifting problem Kontogeorgis, Aristides Terezakis, Alexios Algebraic Geometry Number Theory 14H37, 20C20, 20C10, 14H10, 13D02, 14D15 We are investigating the lifting problem for local actions involving semidirect products of a cyclic $p$-group with a cyclic group prime to $p$, where $p$ represents the characteristic of the special fiber. We establish a criterion based on the Harbater-Katz-Gabber compactification of local actions, enabling us to determine whether a given local action can be lifted or not. Specifically, in the case of the dihedral group, we present an example of a local dihedral action that cannot be lifted. This instance provides a more potent obstruction than the KGB obstruction. |
| title | An obstruction to the local lifting problem |
| topic | Algebraic Geometry Number Theory 14H37, 20C20, 20C10, 14H10, 13D02, 14D15 |
| url | https://arxiv.org/abs/2304.08377 |