格罗斯-霍普金斯对偶

Gross-Hopkins Duals of Higher Real K-theory Spectra

We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain finite subgroups $G$ of the Morava stabilizer group, the homotopy fixed point spectra $E_n^{hG}$ are Gross-Hopkins self-dual up to a shift. In this paper, we determine the shift for those finite subgroups $G$ which contain $p$-torsion. This generalizes previous results for $n=2$ and $p=3$.

The Lubin-Tate stack and Gross-Hopkins duality

Morava $E$-theory $E$ is an $E_\infty$-ring with an action of the Morava stabilizer group $Γ$. We study the derived stack $\operatorname{Spf} E/Γ$. Descent-theoretic techniques allow us to deduce a theorem of Hopkins-Mahowald-Sadofsky on the $K(n)$-local Picard group, as well as a recent result of Barthel-Beaudry-Stojanoska on the Anderson duals of higher real $K$-theories.

通过Gross-Hopkins对偶性研究奇异Picard群与色消失现象

Exotic Picard groups and chromatic vanishing via the Gross-Hopkins duality

本文利用Gross-Hopkins对偶性研究奇异K(h)-局部Picard群与色消失猜想，证明高度3素数5下奇异元素不可被V(1)检测、同调消失猜想在I_{h-1}模下成立且κₕ为零，为κ₃消失证明奠基。

Gross-Hopkins对偶与Gorenstein条件

Gross-Hopkins duality and the Gorenstein condition

Gross和Hopkins证明了在色稳定同伦中，Spanier-Whitehead对偶与Brown-Comenetz对偶几乎重合。我们的目标是在[代数和拓扑中的对偶性，Adv.Math.200（2006），357- 402]的意义下，根据环谱映射的Gorenstein条件，对这一现象给出概念性解释。arXiv：math.AT/0510247 ]。我们描述了环谱映射的Brown-Comenetz对偶模的一般概念，并证明了在这种情况下，这种对偶模对应于可逆K（n）-局部谱。