An Orientation Map for Height p-1 Real E Theory

Real Orientations of Lubin-Tate Spectra

We show that Lubin-Tate spectra at the prime $2$ are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height $n$, we compute the entire homotopy fixed point spectral sequence for $E_n$ with its $C_2$-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $C_2$-fixed points.

Wilson 空间、Snaith 构造与椭圆定向

Wilson Spaces, Snaith Constructions, and Elliptic Orientations

本文构造了一个典范的偶周期 E_∞-环谱族，每素数 p 和色高度 n 恰有一个成员，通过红移现象用 BP⟨n−1⟩ 产生高度 n 理论，并定向椭圆 Morava E-理论。

Complex orientations and $\text{TP}$ of complete DVRS

Let $L$ be finite extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_L$. I show that periodic topological cyclic homology of $\mathcal{O}_L$, over the base $\mathbb{E}_{\infty}$-ring $\mathbb{S}_{W(\mathbb{F}_q)}[z]$ carries a $p$-height one formal group law mod $p$ that depends on the Eisenstein polynomial of $L$ over $\mathbb{Q}_p$ for a choice of uniformizer $\varpi\in \mathcal{O}_L$.

奇素数类Real定向的类比

Odd primary analogs of Real orientations

本文在$C_p$-等变同伦论中定义了$\mu_p$-定向，推广了Real定向，并证明Morava $E$-理论和$\mathrm{tmf}(2)$分别具有$\mu_p$和$\mu_3$定向，通过单个等变映射生成其同伦，揭示高度移位现象。

Obstruction theory and the level $n$ elliptic genus

Given a height $\leq 2$ Landweber exact $\mathbb{E}_\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\mathbb{E}_\infty$-complex orientation $\mathrm{MU} \to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\mathbb{E}_\infty$-complex orientation $\mathrm{MU} \to \mathrm{tmf}_1 (n)$ for all $n \geq 2$.

The sigma orientation is an H-infinity map

In "Elliptic spectra, the Witten genus, and the Theorem of the cube" (Invent. Math. 146 (2001)), the authors constructed a natural map from the Thom spectrum MU<6> to any elliptic spectrum, called the "sigma orientation". MU<6> is an H-infinity ring spectrum, and in this paper we show that if E is a K(2)-local H-infinity elliptic spectrum, then the sigma orientation is a map of H-infinity spectra.