9 problems

Classification conjecture. Then $\varphi$ is a Pfister neighbour.

Vishik–Hoffmann conjectures. The following assertions should hold:

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

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

Let $F$ be a field, let $I^n(F)$ denote the $n$th power of the fundamental ideal in the Witt ring of $F$, and let $u$-fold Pfister forms be tensor products of $u$ binary forms. A…

Pfister involution conjecture.

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

Expected height-two classification. Exactly one of the following holds:

Hoffmann's maximal splitting conjecture. If $q$ has maximal splitting, then $q$ is a Pfister neighbour.