Formal Manifold Structures on Positive Characteristic Varieties

Runjie Hu; Siqing Zhang

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arXiv · 2504.17221

Formal Manifold Structures on Positive Characteristic Varieties

Runjie Hu·Siqing Zhang

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Abstract

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.

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BibTeX RIS

Runjie Hu, Siqing Zhang. 2025-04-24. Formal Manifold Structures on Positive Characteristic Varieties. https://arxiv.org/abs/2504.17221

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