6 problems

In the Morel--Voevodsky model, let $X$ be a finite ${\rm C}_2$-space, and let … be the natural map from fixed points to homotopy fixed points induced by coarse sheafification. The…

Let $E_h$ be Morava $E$-theory at a prime $p$, with coefficient ring … Let $\mathbb{S}_h$ denote the Morava stabilizer group, and let $G\subseteq\mathbb{S}_h$ be a finite subgroup.…

Let $k$ be a perfect field, let $G=\operatorname{Gal}(\bar{k}/k)$, and let $\mathbf{H}^{\mathbb{A}^1}\mathbb{Q}$ denote rational $\mathbb{A}^1$-homology. Let $\mathcal{X}$ be an…

The $2$-adic Lichtenbaum–Quillen conjecture. This map is an isomorphism for $n\geq \dim X-1$ and an injection for $n\geq \dim X-2$.

Let $K(n)$ denote the height-$n$ Morava $K$-theory, let $L_{K(n)}S^0$ be the $K(n)$-local sphere, and let $\mathbb{Z}_p$ be the ring of $p$-adic integers. Finite-generation conject…

Let $G$ be a finite $p$-group and let $X$ be a bounded below $G$-spectrum of finite type mod$p$. Write $X^G$ for its $G$-fixed points and $X^{hG}$ for its $G$-homotopy fixed points…