Profinite Etale Cobordism

Stable etale realization and etale cobordism

We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an étale topological realization of the stable motivic homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero. On the other hand we get a natural setting for étale cohomology theories. In particular, we define and discuss an étale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from étale cohomolog…

Torsion algebraic cycles and etale cobordism

Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of $\ell$-adic étale cobordism over an algebraically closed field of positive characteristic. This shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah, Hirzebruch and Totaro also work in positive characteristic.

有限群的Borel完备性与光滑Artin动机

Profinite Borel completeness and smooth Artin motives

本文研究有限群的Borel完备性与光滑Artin动机，探讨了有限群和 profinite 群的Borel完备性概念，并通过Voevodsky定理扩展了Nisnevich情况下的光滑Artin动机与Bredon上同调谱的关系。

Algebraic Cobordism and Étale Cohomology

Thomason's étale descent theorem for Bott periodic algebraic $K$-theory \cite{aktec} is generalized to any $MGL$ module over a regular Noetherian scheme of finite dimension. Over arbitrary Noetherian schemes of finite dimension, this generalizes the analog of Thomason's theorem for Weibel's homotopy $K$-theory. This is achieved by amplifying the effects from the case of motivic cohomology, using the slice spectral sequence in the case of the universal example of algebraic cobordism. We also obtain integral versions of these statements: Bousfield localization at étale motivic cohomology is the …

具有有限基本群的正特征簇提升的一个必要条件

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups

研究具有有限基本群的正特征簇提升到特征零的必要条件，基于平展同伦理论和沃尔有限性障碍，通过定义模l有限支配性概念，证明簇提升的链复形条件，还扩展了沃尔有限性障碍讨论。

Verdier hypercovering theorem for motivic spectra

We prove a Verdier Hypercovering Theorem for cohomology theories arising from motivic spectra. This allows us to construct for smooth quasi-projective complex varieties a natural morphism from etale algebraic to Hodge filtered complex cobordism, which extends the map from etale motivic to Deligne-Beilinson cohomology.