13 problems

Periodicity conjecture. These $h_0$-submodules have the same $h_0$-coexponent for all $i$.

Let $\mathcal A$ be the mod-two Steenrod algebra, let $s\geqslant0$, and set … Let $P$ denote the Adams periodicity operator, and let $h_i$, $g_i$, $f_i$, $c_i$, $D_2$ and the disp…

Let $E_2$ denote the Adams $E_2$ page for the sphere, viewed with its algebraic structure, and let its differentials be regarded as derivations. Uniqueness conjecture. The space of…

Collapse conjecture. The spectral sequence collapses at the $E_9$ page. This would determine the localized cohomology after the computed differentials through $E_9$, and is propose…

New Doomsday Conjecture. For any $Sq^0$-family in $\operatorname{Ext}_{A_*}(\mathbb{F}_2,\mathbb{F}_2)$, only finitely many elements survive to the $E_\infty$-page of the classical…

Let $s$ be an Adams filtration and let $\operatorname{Ext}^{s,t}_{\mathcal{A}_*}(\mathbb{F}_2,\mathbb{F}_2)$ denote the corresponding Ext groups of the dual Steenrod algebra. The D…

Let $X$ be a pointed CW-complex, let $Q_0X$ denote the basepoint component of $QX=\Omega^\infty\Sigma^\infty X$, and let $H:\pi_*(Q_0X)\to H_*(Q_0X)$ be the Hurewicz homomorphism,…

Let $p$ be an odd prime, let $A$ be the mod $p$ Steenrod algebra, and let $\varphi_s$ denote the mod $p$ Lannes–Zarati homomorphism in Adams filtration $s$, with positive stem $t$.…

Let $\mathcal{B}_{(n)}$ denote the algebra of $(n+1)$-st order mod $p$ cohomology operations, with $n\geq 0$. For $n=0$, $\mathcal{B}_{(0)}=\mathcal{A}$ is the mod $p$ Steenrod alg…

Let $p\geq 5$ and $s\leq 4$. Suppose … with the stated additional vanishing assumptions. If $d_2(x)=a_0x'\in Ext_A^{s+2,tq+1}(\mathbb Z_p,\mathbb Z_p)$, where…

Let $p\geq 7$, $n\geq 3$, and $3\leq s<p$. Let $\widetilde{\gamma}_s$ be the class used in the preceding results, and let … Conjecture 9.6.8. The products…

Let $p\geq 7$ and $n\geq 3$. Let $k_n\in Ext_A^{2,2p^{n+1}q+p^nq}(\mathbb Z_p,\mathbb Z_p)$ and $l'_n\in Ext_A^{3,2p^{n+1}q+p^nq}(\mathbb Z_p,\mathbb Z_p)$. Conjecture 9.5.5. There…

Let $x_j([k,l])$ be the coefficients in a simultaneous solution of the relations defining the dualized Hopf algebra, and let $\zeta_i$ denote the associated generators. Conjectural…