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math.KT2022
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…
math.KT2022
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…
math.AT2022
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…