Formal Manifold Structures on Positive Characteristic Varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912593653792768 |
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| author | Hu, Runjie Zhang, Siqing |
| author_facet | Hu, Runjie Zhang, Siqing |
| contents | In his 1970 ICM report, Sullivan proposes the program of l-adic formalization of the concept of manifolds. In this program, he claims that smooth positive characteristic varieties should carry l-adic formal manifold structures. He also claims the existence of an abelianized Galois symmetry on l-adic formal manifold structures. This paper carries out this program, establishes the claims for certain varieties, and relates the abelianized Galois symmetry on l-adic formal manifold structures to the Galois symmetry of varieties. Meanwhile, we prove that a simply-connected variety is l-adic homotopic equivalent to a simply-connected finite CW complex if and only if the l-profinite completion of its etale homotopy type admits an l-local lifting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal Manifold Structures on Positive Characteristic Varieties Hu, Runjie Zhang, Siqing Algebraic Topology Algebraic Geometry Geometric Topology In his 1970 ICM report, Sullivan proposes the program of l-adic formalization of the concept of manifolds. In this program, he claims that smooth positive characteristic varieties should carry l-adic formal manifold structures. He also claims the existence of an abelianized Galois symmetry on l-adic formal manifold structures. This paper carries out this program, establishes the claims for certain varieties, and relates the abelianized Galois symmetry on l-adic formal manifold structures to the Galois symmetry of varieties. Meanwhile, we prove that a simply-connected variety is l-adic homotopic equivalent to a simply-connected finite CW complex if and only if the l-profinite completion of its etale homotopy type admits an l-local lifting. |
| title | Formal Manifold Structures on Positive Characteristic Varieties |
| topic | Algebraic Topology Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2504.17221 |