论文标题
代数$ k $ - 理论和代数的恢复几乎数学
Algebraic $K$-theory and algebraic cobordism of almost mathematics
论文作者
论文摘要
恶魔； Gabber和Ramero几乎引入了数学。从另一种方面来说，几乎可以表征数学的表征，是Quillen未发表的注释中提到的模块的双关化类别。本文将Quillen的双向化概念应用于Gabber和Ramero的作品，建立了几乎是代数$ K $ - 理论和COBORDISM的版本。由于几乎$ k $ - 理论，我们证明，在几乎包含一个字段的几乎代数的情况下，几乎$ k $ - 几乎是代数的理论是该领域$ k $的直接因素，这意味着几乎$ k $ - 理论占用了Gersten财产。我们澄清说，几乎$ k $ - 理论是$ k $ - $ k $的理论谱系，就quillen而言。此外，我们获得的是，几乎代数的共同体在零段稳定的稳定整体完美素代代数具有有限的语法拓扑结构上具有倾斜等效性。
Faltings; Gabber and Ramero introduced almost mathematics. In another way, almost mathematics can be characterized bilocalization abelian category of modules mentioned in Quillen's unpublished note. Applying the concept of Quillen's bilocalization to Gabber and Ramero's work, this paper establishes the almost version of algebraic $K$-theory and cobordism. As a result of almost $K$-theory, we prove that in the case an almost algebra containing a field, the almost $K$-theory of the almost algebra is a direct factor of the $K$-theory of the field, implying that almost $K$-theory holds the Gersten property. We clarify that an almost $K$-theory is a $K$-theory spectrum of non-unital firm algebras in the sense of Quillen. Furthermore, we obtain that almost algebraic cobordism holds tilting equivalence on the category of zero-section stable integral perfectoid algebras with finite syntomic topology.
