Finite syntomic topology and algebraic cobordism of non-unital algebras

2022/03/10 by Kato, Yuki · 1 citation
#14F42 (primary) #18N40 (secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.05331

Abstract

Elmanto, Hoyois, Khan, Sosnilo, and Yakerson invented that the algebraic cobordism is the sphere spectrum of the ℙ¹₊-stable homotopy category of framed motivic spectra with finite syntomic correspondence. Inspired by their works and Dwyer--Kan's hammock localization, we consider the localization of the stable ∞-category of motivic spectra by zero-section stable finite syntomic surjective morphisms. This paper results that the localization functor is \mathbbA¹-homotopy equivalent to the finite syntomic hyper-sheafification, and the algebraic cobordism is weakly equivalent to the motivic sphere spectrum after the localization (or the hyper-sheafification). Furthermore, on the finite syntomic topology, we prove the tilting equivalence between the algebraic cobordisms for non-unital integral perfectoid algebras.

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• Tilting equivalence of finite almost derived algebraic cobordism for perfectoid algebras

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