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math.CT2025
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…
math.CT2023
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…
math.CT2023
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…
math.CT2023
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…