论文标题
非阴谋代数$ k $ - 理论和几乎数学
Non-unital algebraic $K$-theory and almost mathematics
论文作者
论文摘要
Gersten的猜想仍然是代数$ K $ - 混合特征离散估值环理论的一个空旷的问题。在本文中，我们建立了非突起代数$ k $ - 修改为从非积极代数到稳定的稳定类别的确切函数 $ \ infty $ - 光谱类别。我们证明，对于任何几乎UNITAL代数，非UNITAL $ k $ - 理论将同型分解为非潜水$ k $ - 理论 - 相应的理想和残留代数，这意味着非附带$ k $的gersten属性 - 相应理想的理想。
The Gersten conjecture is still an open problem of algebraic $K$-theory for mixed characteristic discrete valuation rings. In this paper, we establish non-unital algebraic $K$-theory which is modified to become an exact functor from the category of non-unital algebras to the stable $\infty$-category of spectra. We prove that for any almost unital algebra, the non-unital $K$-theory homotopically decomposes into the non-unital $K$-theory the corresponding ideal and the residue algebra, implying the Gersten property of non-unital $K$-theory of the the corresponding ideal.
