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Unramified $F$–divided
objects and the étale fundamental pro-groupoid in positive
characteristic
Yuliang Huang, Giulio Orecchia and Matthieu Romagny |
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Geometry & Topology 26 (2022) 3221–3306
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Abstract |
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Let be a flat algebraic stack of finite presentation. We define a new étale fundamental pro-groupoid , generalizing Grothendieck’s enlarged étale fundamental group from SGA 3 to the relative situation. When is of equal positive characteristic , we prove that naturally arises as colimit of the system of relative Frobenius morphisms in the pro-category of Deligne Mumford stacks. We give an interpretation of this result as an adjunction between and the stack of –divided objects. In order to obtain these results, we study the existence and properties of relative perfection for algebras in characteristic . |
Keywords
relative Frobenius, $F$–divided object, perfection,
coperfection, étale fundamental group, étale affine hull
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Mathematical Subject Classification
Primary: 13A35, 14D23, 14F35, 14G17
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References |
Publication
Received: 19 February 2021
Revised: 6 August 2021
Accepted: 4 September 2021
Published: 23 January 2023
Proposed: Dan Abramovich
Seconded: Richard P Thomas, Marc Levine
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Authors |
| Yuliang Huang | |
| Chengdu Research Institute Huawei Technology Chengdu China |
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| Giulio Orecchia | |
| École polytechnique fédérale de
Lausanne Lausanne Switzerland |
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| Matthieu Romagny | |
| CNRS, IRMAR – UMR 6625 Université de Rennes 1 Rennes France |
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