arXiv Open Access 2022

Non-unital algebraic $K$-theory and almost mathematics

Yuki Kato

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.KT math.CT

Penulis (1)

Yuki Kato

Format Sitasi

APA MLA BibTeX

Kato, Y. (2022). Non-unital algebraic $K$-theory and almost mathematics. https://arxiv.org/abs/2207.08378

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓