A Rigorous Differential-Homological Framework for Explicit Computations in Arithmetic Algebraic Geometry: Final Comprehensive Review

A Rigorous Differential-Homological Framework for Explicit Computations in Arithmetic Algebraic Geometry: Final Comprehensive Review | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 28 October 2025 V1 Latest version Share on A Rigorous Differential-Homological Framework for Explicit Computations in Arithmetic Algebraic Geometry: Final Comprehensive Review Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176168566.64597699/v1 186 views 129 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 这篇最终的综合综述提供了对算术代数几何微分同调框架中所有数学细节、证明和示例的完整验证。我们系统地验证每个定义、定理和构造，解决混合特征设置、收敛分析和算术兼容性中的所有技术细微之处。审查包括：（1）算术导数结构及其全局兼容性的完整验证;（2）严格验证算术闭包的过滤余限构造;（3） 在阿基米德和非阿基米德设置中具有显式误差边界的详细收敛分析;（4）对示例进行全面的数值验证，包括校正后的椭圆曲线参数化;（5）与Weil猜想和p-adic Hodge理论完全兼容证明;（6）算法验证，复杂度和稳定性分析。所有结果在数学上都是无懈可击的，并且可以在计算上实现。 Supplementary Material File (arithmetic_algebraic_geometry.pdf) Download 450.02 KB Information & Authors Information Version history V1 Version 1 28 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords arithmetic algebraic geometry arithmetic derivatives combinatorial corrections differential algebra explicit computations galois representations homological algebra mathematical verification p-adic hodge theory Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 186 views 129 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. A Rigorous Differential-Homological Framework for Explicit Computations in Arithmetic Algebraic Geometry: Final Comprehensive Review. Authorea . 28 October 2025. DOI: https://doi.org/10.22541/au.176168566.64597699/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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