Truncated resolution model structures

Redshift and multiplication for truncated Brown-Peterson spectra

We equip $\mathrm{BP} \langle n \rangle$ with an $\mathbb{E}_3$-$\mathrm{BP}$-algebra structure, for each prime $p$ and height $n$. The algebraic $K$-theory of this ring is of chromatic height exactly $n+1$, and the map $\mathrm{K}(\mathrm{BP}\langle n \rangle)_{(p)} \to \mathrm{L}_{n+1}^{f} \mathrm{K}(\mathrm{BP}\langle n\rangle)_{(p)}$ has bounded above fiber.

On truncated quasi-categories

For each $n \geq -1$, a quasi-category is said to be $n$-truncated if its hom-spaces are $(n-1)$-types. In this paper we study the model structure for $n$-truncated quasi-categories, which we prove can be constructed as the Bousfield localisation of Joyal's model structure for quasi-categories with respect to the boundary inclusion of the $(n+2)$-simplex. Furthermore, we prove the expected Quillen equivalences between categories and $1$-truncated quasi-categories and between $n$-truncated quasi-categories and Rezk's $(n,1)$-$Θ$-spaces.

群胚性与截断的 $n$-拟范畴

Groupoidal and truncated $n$-quasi-categories

本文定义了群胚性与截断的 $n$-拟范畴，证明其为特定模型结构的纤维对象，并建立其与单纯集上空间模型的 Quillen 等价关系，同时构造了柱对象。

The Bousfield lattice for truncated polynomial algebras

The global structure of the unbounded derived category of a truncated polynomial ring on countably many generators is investigated, via its Bousfield lattice. The Bousfield lattice is shown to have cardinality larger than that of the real numbers, and objects with large tensor-nilpotence height are constructed.

A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials

The main result of this paper is to calculate the Batalin-Vilkovisky structure of $HH^*(C^*(\mathbf{K}P^n;R);C^*(\mathbf{K}P^n;R))$ for $ \mathbf{K}=\mathbb{C}$ and $\mathbb{H}$, and $R=\mathbb{Z}$ and any field; and shows that in the special case when $M=\mathbb{C}P^1=S^2$, and $R=\mathbb{Z}$, this structure can not be identified with the BV-structure of $\mathbb{H}_*(LS^2;\mathbb{Z})$ computed by Luc Memichi in \cite{menichi2}. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas \cite{felix--thomas}, the…

复几何中截断多重复形的模型范畴结构

Model category structures on truncated multicomplexes for complex geometry

本文在 N-多重复形上构造了一族模型范畴结构，其弱等价由两个谱序列的固定页上的拟同构刻画，从而为研究近复与广义复流形的同伦型提供基础。