布朗-彼得森塔中的非 torsion 非代数类

Examples of non-algebraic classes in the Brown-Peterson tower

For every $n\ge 0$, we construct classes in the Brown-Peterson cohomology $BP\langle n \rangle$ of smooth projective complex algebraic varieties which are not in the image of the cycle map from the corresponding motivic Brown-Peterson cohomology. This generalizes the examples of Atiyah and Hirzebruch to all finite levels in the Brown-Peterson tower.

Commutativity conditions for truncated Brown-Peterson spectra of height 2

An algebraic criterion, in terms of closure under power operations, is determined for the existence and uniqueness of generalized trun- cated Brown-Peterson spectra of height 2 as E_\infty-ring spectra. The criterion is checked for an example at the prime 2 derived from the universal elliptic curve equipped with a level Γ_1(3)-structure.

Unstable splittings in Hodge filtered Brown-Peterson cohomology

We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown-Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson's unstable splitting. As a consequence, we obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology for complex manifolds.

稳定A^1-同伦理论中的Brown-Peterson谱

Brown-Peterson spectra in stable A^1-homotopy theory

我们通过$E^{**}$的“拓扑”子环$E^{*}=\oplus_iE^{2i,i}$上的形式群律刻画了从代数配边谱$\QTR{Bbb}{MGL}$（\QCITE{cite}{}{Vo1}）到定向谱$\QTR{Bbb}{E}$（Morel \QCITE{cite}{}{Mo}意义下）的环谱态射.然后利用这个结果构造了任意素数$p$在$\QTR{Bbb}{MGL}_{(p)}$上的基元Quillen幂等元.这定义了与素$p$相关联的$BP$ -谱，如Quillen的\QCITE{cite}{}{Q1}中用于面向复数的拓扑情况。

提升到截断Brown-Peterson谱与特征$p>0$中的Hodge-de Rham退化

Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$

本文证明在特定条件下，光滑正常$\nmathbf{F}_p$概形的Hodge-de Rham退化成立，条件涉及拟凝聚层范畴提升到截断Brown-Peterson谱及HKR谱序列在$E_2$页退化，方法为非交换版本，与Mathew的论证类似。

Topological Hochschild homology, truncated Brown-Peterson spectra, and a topological Sen operator

In this article, we study the topological Hochschild homology of $\mathbf{E}_3$-forms of truncated Brown-Peterson spectra, taken relative to certain Thom spectra $X(p^n)$ (introduced by Ravenel and used by Devinatz-Hopkins-Smith in the proof of the nilpotence theorem). We prove analogues of Bökstedt's calculations $\mathrm{THH}(\mathbf{F}_p) \simeq \mathbf{F}_p[ΩS^3]$ and $\mathrm{THH}(\mathbf{Z}_p) \simeq \mathbf{Z}_p[ΩS^3\langle{3}\rangle]$. We also construct a topological analogue of the Sen operator of Bhatt-Lurie-Drinfeld, and study a higher chromatic extension. The behavior of these "top…