Loops on schemes and the algebraic fundamental group
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866914716234809344 |
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| author | Rülling, Kay Schröer, Stefan |
| author_facet | Rülling, Kay Schröer, Stefan |
| contents | In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval from topology by what we call interval schemes. This leads to an algebraic version of continuous loops, and the homotopy relation is defined in terms of the monodromy action. Our main results hinge on Macaulayfication for proper schemes and Lefschetz type results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11364 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Loops on schemes and the algebraic fundamental group Rülling, Kay Schröer, Stefan Algebraic Geometry 14F35, 14E20, 14H30 In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval from topology by what we call interval schemes. This leads to an algebraic version of continuous loops, and the homotopy relation is defined in terms of the monodromy action. Our main results hinge on Macaulayfication for proper schemes and Lefschetz type results. |
| title | Loops on schemes and the algebraic fundamental group |
| topic | Algebraic Geometry 14F35, 14E20, 14H30 |
| url | https://arxiv.org/abs/2109.11364 |