23 problems

Let $G$ be a compact Lie group, let $H<G$ be a closed subgroup, and let $X$ and $Y$ be $H$-equivariant $\mathcal{D}_V$-algebras whose underlying $H$-equivariant orthogonal spectra…

Let $G$ be a compact Lie group, let $K<H<G$, and let $X$ be a $K$-equivariant little $T_{eK}(G/K)$-disk algebra whose underlying $K$-equivariant orthogonal spectrum is cofibrant in…

Let $G$ be a compact Lie group, let $K<H<G$, and let $X$ be a $K$-equivariant little $T_{eK}(G/K)$-disk algebra. Let $D(T_{eH}(G/H))$ be the open unit disk and let $i^*$ denote the…

Let $G$ be a compact Lie group, let $H<G$ be a closed subgroup, let $K\trianglelefteq G$ be normal, and let $X$ be an $H$-equivariant $\mathcal{D}_V$-algebra satisfying the paper's…

Let $G$ be a compact Lie group, let $H<G$ be a closed subgroup, and let $R$ be a cofibrant $H$-equivariant commutative ring orthogonal spectrum in the $U_H$-universe model structur…

Let $G$ be a compact Lie group, let $H<G$ be a closed subgroup, and let $N_H^G$ be the point-set relative norm indexed on universes $U_H$ and $U$. Suppose $X'$ and $X$ satisfy the…

Let $G$ be a compact Lie group, let $K<G$ be finite, and let $N$ be the normalizer of $K$ in $G$. Let $X$ be an input for the norm $N_e^G$. Normalizer geometric fixed-point conject…

Let $G$ be a compact Lie group, let $K<G$ be finite, and let $X$ be an input for the norm $N_e^G$. Assume that the adjoint action of $K$ on $T_eG$ is trivial, so that…

Let $G$ be a compact Lie group, let $K<G$ be a closed subgroup of positive dimension, and let $X$ be a $\mathcal{D}^{d}$-algebra whose underlying orthogonal spectrum is cofibrant,…

Let $G$ be a compact Lie group, let $R$ be a cofibrant commutative algebra, and let $U$ and $U^{G}$ denote the relevant complete universes. Write $N_e^G R$ for the norm and…

Let $G$ be a group such that the classifying space for proper $G$-actions, $\underline{E}G$, has a finite model. Let $A_{\operatorname{ho}}(G)=\pi_G^0(\underline{E}G)$, let…

Strict cyclotomic Deligne conjecture. For every natural number $n$, the following diagram of genuine $S^1$-spectra commutes:

Let $G$ be a finite group and let $\mathrm{AN}^{RO}_G(\mathbb S)$ be the $RO(G)$-filtered Adams--Novikov object. Applying the totalization functor gives the filtered $G$-spectrum…

Multiplicative tom Dieck splitting conjecture. There exists a multiplicative structure $\Xi$ such that $\Xi$-algebras are in particular $G$-$E_{\infty}$ algebras and, in the augmen…

Untwisted multiplication conjecture. The maps constructed from the monoidal structure make $\widetilde{\Theta^n}F$ into a nonunital $E_\infty$-ring spectrum.

Let $G$ be a finite $p$-group, let $E$ be a $p$-complete complex-oriented spectrum with associated formal group of height $n$, and let $E^2(f)$ denote the induced map in degree-two…

Classical blue-shift phenomenon. The spectrum $t_{G}({\rm \inf}^G_{e}(E))^G$ is $v_{n-s_{G;E}}$-periodic for some positive integer $s_{G;E}$. When $s_{G;E}>n$, the $v_{n-s_{G;E}}$-p…

Consider the $\operatorname{\mathop{\rm Ext}}$ groups in the $\rho$-Bockstein spectral sequence … Here, the power of $\tau$ is the exponent of $\tau$ in the relevant…

Let $p$ be a prime, let $A$ be a finite abelian $p$-group, and let $\mathcal{F}$ be a proper family of subgroups of $A$. Let $R$ be a commutative algebra regarded as a Borel-equiva…

Let $C_2$ be the cyclic group of order two, and let $\mathrm{tmf}_{C_2}$ be the homotopy pullback spectrum defined by the Tate diagram described above. A $C_2$-ring spectrum means…

The $\log_p$-conjecture. For all $n\geq r$, one has

Equivariant generating hypothesis. The restriction of $\underline{\pi}_*^G(-)$ to the subcategory of finite $G$-spectra is faithful. Equivalently, if a map $f:X\to Y$ between finit…

Let $G$ be a finite group. Write $\operatorname{\sf StHom}^{naive}(G)$ and $\operatorname{\sf StHom}(G)$ for the categories of naive and genuine $G$-spectra, respectively, and let…