论文标题
有限的语法拓扑结构和代数代数的代数核论
Finite syntomic topology and algebraic cobordism of non-unital algebras
论文作者
论文摘要
Elmanto，Hoyois，Khan，Sosnilo和Yakerson发明的是代数的COBORDISM是$ \ Mathbb {p}^1 _+$ - 稳定的同型类别的$ \ mathbb {p}^1 _+$ - 带有有限语义对应关系的稳定同型类别。受其作品和dwyer的启发 - 肯尼的吊床本地化，我们考虑了稳定的$ \ infty $ - 动机光谱的本地化，零部分稳定的有限语义旋转形态。本文导致定位函子为$ \ mathbb {a}^1 $ - 示例术等效于有限的构想超声层化，而代数的同时性则弱等同于动机球体谱图（或超副总成）。此外，在有限的构想拓扑结构上，我们证明了代数核心对非非联合整合整体完美代数代数的倾斜等效性。
Elmanto, Hoyois, Khan, Sosnilo, and Yakerson invented that the algebraic cobordism is the sphere spectrum of the $\mathbb{P}^1_+$-stable homotopy category of framed motivic spectra with finite syntomic correspondence. Inspired by their works and Dwyer--Kan's hammock localization, we consider the localization of the stable $\infty$-category of motivic spectra by zero-section stable finite syntomic surjective morphisms. This paper results that the localization functor is $\mathbb{A}^1$-homotopy equivalent to the finite syntomic hyper-sheafification, and the algebraic cobordism is weakly equivalent to the motivic sphere spectrum after the localization (or the hyper-sheafification). Furthermore, on the finite syntomic topology, we prove the tilting equivalence between the algebraic cobordisms for non-unital integral perfectoid algebras.
