On Galois categories and condensed contractible schemes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918494194368512 |
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| author | Mair, Catrin |
| author_facet | Mair, Catrin |
| contents | We extend the study of the condensed Galois category of a scheme introduced by Barwick, Glasman and Haine in their work on Exodromy. We elaborate its connection to Lurie's work on Ultracategories and provide a description in terms of w-contractible rings. We give a classification of schemes whose Galois category has an initial, respectively, a terminal object. This implies the condensed homotopy type of the scheme, which was studied in more detail in [arXiv:2510.07443v1], to be trivial. Furthermore, we compute a formula for the (underlying group of the) condensed fundamental group of a general Dedekind domain and show that it is non-trivial for the spectrum of the integers Spec(Z).This means that Spec(Z) is not condensed contractible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Galois categories and condensed contractible schemes Mair, Catrin Algebraic Geometry Algebraic Topology Category Theory 14F35, 14F20 We extend the study of the condensed Galois category of a scheme introduced by Barwick, Glasman and Haine in their work on Exodromy. We elaborate its connection to Lurie's work on Ultracategories and provide a description in terms of w-contractible rings. We give a classification of schemes whose Galois category has an initial, respectively, a terminal object. This implies the condensed homotopy type of the scheme, which was studied in more detail in [arXiv:2510.07443v1], to be trivial. Furthermore, we compute a formula for the (underlying group of the) condensed fundamental group of a general Dedekind domain and show that it is non-trivial for the spectrum of the integers Spec(Z).This means that Spec(Z) is not condensed contractible. |
| title | On Galois categories and condensed contractible schemes |
| topic | Algebraic Geometry Algebraic Topology Category Theory 14F35, 14F20 |
| url | https://arxiv.org/abs/2605.10358 |