2022/07/18 by Kato, Yuki · 1 citation
#14F12 (primary) #18N40 (secondary)} #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2207.08378
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 ∞-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.