9 problems

Spectral-sequence collapse conjecture. For all $F,G\in\mathcal{P}$, this spectral sequence collapses at the second page. In particular, there is a graded isomorphism, not necessari…

Generic cohomology conjecture. For all $F,G\in\mathcal{P}$, there is a graded isomorphism, natural in $F$ and $G$,

Let $\mathbb{K}$ be a field, let $q\in\mathbb{K}^{\times}$ be a non-zero scalar, and let $F$ and $G$ be strict polynomial functors. Write $F^{(1)_q}$ and $G^{(1)_q}$ for their quan…

Let $F$ and $G$ be strict polynomial functors, let $F^{(s)_q}$ and $G^{(s)_q}$ denote their $s$-th quantum Frobenius twists, and define … For each degree $k$, the iterated quantum…

Let $F$ and $G$ be strict polynomial functors, let $F^{(1)_q}$ and $G^{(1)_q}$ denote their quantum Frobenius twists, and let…

Let a topos with natural number object be a topos equipped with a natural number object, and let a monic polynomial with reductions be as considered in the paper. Initial-algebra f…

Let $F_n$ be a free group of rank $n$, and let $IA_n$ be the kernel of the canonical epimorphism ${\rm Aut}(F_n)\twoheadrightarrow GL_n(\mathbb{Z})$. For each $d\in\mathbb{N}$, let…

Let $F_n$ be a free group of rank $n$, and let $IA_n$ be the kernel of the canonical epimorphism ${\rm Aut}(F_n)\twoheadrightarrow GL_n(\mathbb{Z})$. For each $d\in\mathbb{N}$, let…

Weak polynomial degree conjecture. For every nonunital ring $I$ and every integer $n\in\mathbb{N}$, the functor $H_n(\Gamma_I)$ is weakly polynomial of degree at most $2n$.