1 citations · 1 across the 8 of their papers we have counts for
8 papers
Tilting equivalence of finite almost derived algebraic cobordism for perfectoid algebras
Yuki Kato
In this paper, we prove tilting equivalence for the finite almost derived algebraic cobordism spectrum of perfectoid algebras. More precisely, if is…
Nilpotent approximation and completion of -algebra objects of stable symmetric monoidal model categories
Yuki Kato
We develop a nilpotent approximation theory for Smith ideals, extending adic completion for commutative rings to monoid objects in locally presentable symmetric monoidal abelian ca…
Non-unital algebra objects of stable symmetric monoidal model categories by Smith ideal theory
Yuki Kato
This note remarks that the correspondence between non-unital algebras and augmented unital algebras can be derived from Hovey's Smith ideal theory. Applying Smith ideal theory of s…
Almost mathematics of pointed symmetric monoidal model categories by Smith ideal theory
Yuki Kato
This article is a generalization of a result in Quillen's note ``Module theory over non-unital rings'' giving a one-to-one correspondence between bilocalization of abelian categori…
Non-unital algebraic -theory and almost mathematics
Yuki Kato
The Gersten conjecture is still an open problem of algebraic -theory for mixed characteristic discrete valuation rings. In this paper, we establish non-unital algebraic -theo…
Algebraic -theory and algebraic cobordism of almost mathematics
Yuki Kato
Faltings; Gabber and Ramero introduced almost mathematics. In another way, almost mathematics can be characterized bilocalization abelian category of modules mentioned in Quillen's…
Algebraic cobordism via spans
Yuki Kato
We define the algebraic cobordism of -categories equipped with universal line bundle data as an initial oriented functor in the associated span category. In the standard mo…
Motivic classifying -topoi and spectral stacks
Yuki Kato
In this paper, we develop motivic derived algebraic geometry, an enhancement of derived algebraic geometry adapted to the -homotopy theory of Morel and Voevodsky. We…