Differential Algebraic Methods in Derived Algebraic Geometry: A Rigorous Foundation for Explicit Parameterizations of Derived Stacks

2025 · doi:10.22541/au.176168567.75381174/v1
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Abstract

本文开发了一个严格的微分代数框架，用于对派生代数堆栈和更高几何对象进行显式参数化。在经典微分代数和现代推导代数几何的基础上，我们使用富含同位数据的函数场的微分扩展为推导代数簇构建显式局部参数化。关键创新是系统地使用从推导的切线复数和高阶无穷小邻域的几何形状中得出的组合校正项。我们为主要定理提供完整的证明，详细的例子包括推导的椭圆曲线和推导的ADE奇点，并进行了完整的验证，并与经典理论和推导理论建立了精确的联系。该框架提供了新的计算工具，同时保持了完整的数学严谨性。我们的方法连接了微分代数、派生几何和计算数学，在适当构造的微分派生闭包中提供显式参数化。 Supplementary Material File (derived_algebraic_geometry.pdf) - Download - 433.84 KB Information & Authors Information Version history Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

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Authors Metrics & Citations Metrics Article Usage 291views 128downloads Citations Download citation Dongqi Liu, shifa liu. Differential Algebraic Methods in Derived Algebraic Geometry: A Rigorous Foundation for Explicit Parameterizations of Derived Stacks. Authorea. 28 October 2025. DOI: https://doi.org/10.22541/au.176168567.75381174/v1 DOI: https://doi.org/10.22541/au.176168567.75381174/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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last seen: 2026-05-20T01:45:00.602351+00:00