10 problems

Let $F$ be a field with $|cdot F/cdot F^2|=2^n$, so that $E=E_n\cong (\mathbb Z/2)^n$, and let ${\mathcal G}_F$ be the associated $W$-group. Let…

Vishik's conjecture. There is some $i\in\{1,2,\dots,n+1\}$ such that

Let $W(k)$ be the Witt ring of quadratic forms over a field $k$, with $I\subset W(k)$ the ideal of even-dimensional forms. For an element $x\in W(k)$, let its degree be the natural…

Weak Elementary Type Conjecture. Every finite quaternionic structure that is realized by a field is of elementary type.

Elementary Type Conjecture. Every finite quaternionic structure is of elementary type.

Elementary Type Conjecture. Every finitely generated Witt ring is of elementary type.

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…

Let $(R,G)$ be an abstract Witt ring, called realisable if it arises from a field $F$ of characteristic different from $2$ with $R\cong W(F)$ and $G\cong F^\times/(F^\times)^2$, an…

Let $F$ be a field of characteristic different from $2$, and let $I^nF$ denote the $n$-th power of the fundamental ideal in the Witt ring of $F$. Say that $I^nF$ is $m$-linked if e…

Let $F$ be a field of characteristic different from $2$, let $\varphi$ be an anisotropic quadratic form over $F$, and let $F(\varphi)$ be the function field of its projective quadr…