Carlson, Magnus and Haine, Peter J. and Wolf, Sebastian (2025) A generalization of Voevodsky's reconstruction theorem of schemes from their étale topoi. SELECTA MATHEMATICA-NEW SERIES, 31 (4): 65. ISSN 1022-1824, 1420-9020
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Let k be a field that is finitely generated over its prime field. In Grothendieck's anabelian letter to Faltings, he conjectured that sending a k-scheme to its & eacute;tale topos defines a fully faithful functor from the localization of the category of finite type k-schemes at the universal homeomorphisms to a category of topoi. By extending results of Voevodsky, we prove Grothendieck's conjecture for infinite finitely generated fields of arbitrary characteristic. In characteristic 0, this shows that seminormal finite type k-schemes can be reconstructed from their & eacute;tale topoi, generalizing work of Voevodsky. In positive characteristic, this shows that perfections of finite type k-schemes can be reconstructed from their & eacute;tale topoi.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Aug 2026 06:49 |
| Last Modified: | 11 Aug 2026 06:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67137 |
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