通过紧化同伦与对应关系的严格同伦不变性，以及一维基概形上本质光滑概形的纤维
Strict homotopy invariance via compactified homotopies and correspondences, and fibres of essentially smooth schemes over one-dimensional base schemes
AI总结：
本研究发展一维基概形上的紧化对应与同伦技术，阐明Voevodsky严格同伦不变性定理等的特征假设性质，还得到广义动机上同伦Cousin复形相关猜想的类似结论及一类无环性结果。
摘要：
我们发展了一维基概形上的紧化对应与同伦技术，阐明了著名的Voevodsky严格同伦不变性定理及其在任意基域上的framed correspondences（带标架对应）推广中特征假设的完备性与可逆性。这一Voevodsky动机理论核心定理中的假设自研究起源时便被保留，后被纳入Garkusha-Panin提出的更现代的framed motives（带标架动机）理论中。应用该技术，我们还得到了域上广义动机上同伦的Cousin复形的Gersten猜想与Nisnevich猜想的类似结论，以及一维基概形上本质光滑局部概形的一般纤维上Cousin复形的无环性。
英文摘要：
We develop the technique of compactified correspondences and homotopies over one-dimensional base schemes, and illuminate the perfectness and the inverting of characteristic assumptions from the celebrating Voevodsky's strict homotopy invariance theorem and its framed correspondences generalisation over an arbitrary base field. The assumption in this crucial theorem for Voevodsky's motives theory %over a field was kept from the origins of the study, and came later into more modern theory of framed motives by Garkusha-Panin. Applying the technique, we obtain also analogs of Gersten and Nisnevich conjectures for Cousin complexes of generalised motivic cohomotopies over a field, and acyclicity of Cousin complexes on generic fibres of essentially smooth local schemes over one-dimensional base schemes.
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