16 problems

Let $n=2m$ be a positive integer, and let $f(x)$ be the trinomial defined by equation (1) in the source over ${\mathbb F}_{2^{2m}}$. A pair $(s,t)$ specifies the exponents in this…

Pfister-neighbour conjecture. If $s<\frac{2^{n+1}}{3}$ and $\varphi_1$ is defined over $F$, then $\varphi$ is a Pfister neighbour.

Let $\mathbb K$ be an infinite field, and let $B_1$ and $B_2$ be non-degenerate symmetric $3\times 3$ matrices over $\mathbb K$. The matrices are Lie-equivalent when the Lie algebr…

Let $C$ be a generic hyperelliptic curve of genus $g$ and $2$-rank $0$ over a field of characteristic $2$. Generic automorphism conjecture for 2-rank-zero hyperelliptic curves. If…

Excellent-connections conjecture. For integers $a,b$ with $0\leq a,d_X-b<r$, if $(a,b)$ is excellent, then $a_{\mathrm{lo}}$ and $b^{\mathrm{up}}$ are connected in $\Lambda(X)$.

Refined first-isotropy-index conjecture. If $s<2^u+\mathfrak{i}_1$, then

Hoffmann–Laghribi's conjecture. If $s<2r$ and $\varphi_1$ is defined over $F$, then $\varphi$ is a Pfister neighbour.

Let $\mathcal{D}$ be a finite tensor category over a field $\mathbf{k}$ of characteristic $2$. Let $o(\mathcal{D})$ and $O(\mathcal{D})$ denote its lower and upper Frobenius orders…

Characteristic-two generalization conjecture. Theorem 2 (the equality theorem for alternating bilinear forms) can be generalized to all fields with characteristic $2$.

Let $m\geq2$. A NIS-Lie superalgebra is a Lie superalgebra equipped with a nondegenerate invariant supersymmetric bilinear form. The notation $\widetilde{\mathfrak{po}}(0|2m)$ deno…

Pfister involution conjecture.

Let $L_1(\mathbb{Z}_2)$ be the Lie algebra of polynomial vector fields on the line over the field with two elements, and let $H^*(L_1(\mathbb{Z}_2))$ denote its cohomology algebra.…

Vishik-type isotropy gap conjecture. For every field extension $L/F$, either

Characteristic-two height-two conjecture. There exist a $(d-1)$-fold Pfister form $\pi$ and a $4$-dimensional form $\mathfrak{c}$ of nontrivial determinant such that

Quasi-Pfister divisibility conjecture. The form $\phi$ is divisible by an $(n-1)$-fold quasi-Pfister form.

Assume $p=2$ and $n\ge4$. For a sequence $i=(i_1,\dots,i_l)$, let $a_{i,k}=a_{i_1,k}\dots a_{i_l,k}$; write $i..j$ for the consecutive sequence from $i$ to $j$, and let $L_l[m]$ be…