Smash products of E(1)-local spectra at an odd prime

On the derived functors of destabilization at odd primes

An explicit chain complex is constructed to calculate the derived functors of destabilization at an odd prime, generalizing constructions of Zarati and of Hung and Sum. The methods are based on the ideas of Singer and Miller and also apply at the prime two. A structural result on the derived functors of destabilization is deduced.

The Arone-Goodwillie spectral sequence for $Σ^{\infty}Ω^n$ and topological realization at odd primes

We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at an odd prime.

Cartan公式的一个有效证明：奇素数

An effective proof of the Cartan formula: Odd primes

本文针对奇素数情形，在单纯集中为模p上循环对有效构造自然上边界，从而证明了Cartan公式在上同调中的成立。

The motivic Adams-Novikov spectral sequence at odd primes over $\mathbb{C}$ and $\mathbb{R}$

We study the motivic Adams-Novikov spectral sequence at an odd prime $l$ over the base fields $\mathbb{C}$ and $\mathbb{R}$. This spectral sequence converges to the stable motivic homotopy groups of the $l$-completed motivic sphere spectrum. We show that the spectral sequence is determined by the topological Adams-Novikov sequence, similar to the situation at the prime two over the base field $\mathbb{C}$.

J-Groups of Lens Spaces modulo Odd Prime Powers

We describe the J-Groups of lens spaces modulo odd prime powers via relations and rational representations.

The derived category of complex periodic K-theory localized at an odd prime

We prove that for an odd prime $p$, the derived category $\mathcal{D}(KU_{(p)})$ of the $p$-local complex periodic $K$-theory spectrum $KU_{(p)}$ is triangulated equivalent to the derived category of its homotopy ring $π_*KU_{(p)}$. This implies that if $p$ is an odd prime, the triangulated category $\mathcal{D}(KU_{(p)})$ is algebraic.

奇素数处高阶Adams微分与高阶代数Novikov微分之间的对应

A correspondence between higher Adams differentials and higher algebraic Novikov differentials at odd primes

本文基于“τ的余纤维哲学”，证明了在奇素数处经典Adams谱序列的高阶微分在特定范围内与相应的高阶代数Novikov微分相一致。

The Brown-Peterson spectrum is not $\mathbb{E}_{2(p^2+2)}$ at odd primes

We show that the odd-primary Brown-Peterson spectrum $\mathrm{BP}$ does not admit the structure of an $\mathbb{E}_{2(p^2+2)}$ ring spectrum and that there can be no map $\mathrm{MU} \to \mathrm{BP}$ of $\mathbb{E}_{2p+3}$ ring spectra. We also prove the same results for truncated Brown-Peterson spectra $\mathrm{BP} \langle n \rangle$ of height $n \geq 4$. This extends results of Lawson at the prime $2$.

A Note on the Algebra of Operations for Hopf Cohomology at Odd Primes

Let $p$ be any prime, and let ${\mathcal B}(p)$ be the algebra of operations on the cohomology ring of any cocommutative $\mathbb{F}_p$-Hopf algebra. In this paper we show that when $p$ is odd (and unlike the $p=2$ case), ${\mathcal B}(p)$ cannot become an object in the Singer category of $\mathbb{F}_p$-algebras with coproducts, if we require that coproducts act on the generators of ${\mathcal B}(p)$ coherently with their nature of cohomology operations

奇数素数处的等变 K(1)-局部球面

The equivaraint K(1)-local sphere at odd prime

本文计算了奇数素数处等变 K(1)-局部球面的 RO 分次同伦 Mackey 函子。

Periodic self maps and thick ideals in the stable motivic homotopy category over $\mathbb{C}$ at odd primes

In this article we study thick ideals defined by periodic self maps in the stable motivic homotopy category over $\mathbb{C}$. In addition, we extend some results of Ruth Joachimi about the relation between thick ideals defined by motivic Morava K-theories and the preimages of the thick ideals in the stable homotopy category under Betti realization.

奇素数p的ℤ/p-等变对偶斯廷罗德代数

The $\mathbb{Z}/p$-equivariant dual Steenrod algebra for an odd prime $p$

该研究完全计算了常Mackey函子ℤ/p的RO(ℤ/p)-分次系数Hℤ/p_⋆Hℤ/p，属于代数拓扑领域的相关计算。

奇数素数下 $\mathbb{F}_p$ 的迭代拓扑 Hochschild 同调

Iterated Topological Hochschild Homology of $\mathbb{F}_p$ at odd primes

本文计算奇数素数下 $\mathbb{F}_p$ 的迭代拓扑 Hochschild 同调的同伦群，通过 bar 谱序列证明其在 $E^2$ 页坍缩，并确定环结构。

All p-local finite groups of rank two for odd prime p

In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analisis of the possible saturated fusion systems in terms of the outer automorphism group ant the proper F-radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-local finite group, getting some new examples of these for p = 3.

The smooth Whitehead spectrum of a point at odd regular primes

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum splits off, and the torsion homotopy of the remainder equals the torsion homotopy of the fiber of the restricted S^1-transfer map t: SigmaCP^infty--> S. The homotopy groups of Wh(*) are determined in a range of degrees, and the cohomology of Wh(*) is expressed as an A-module in all degrees, up to an extension. These results have geometric topological interp…

奇素数下Demushkin群的$A_3$-形式性

$A_3$-formality for Demushkin groups at odd primes

该研究针对奇素数下的Demushkin群，探讨微分分次代数的$A_3$-形式性，通过计算Hochschild上同调中的Benson-Krause-Schwede典范类，证明q不变量是否为3决定了其连续上链代数是否满足$A_3$-形式性。