14 problems

Let $F$ be a field, and let $A$ and $B$ be central simple algebras over $F$. Write $SB(A)$ and $SB(B)$ for their associated Severi–Brauer varieties, and let $[A]$ and $[B]$ denote…

Let $k$ be a field, let $d\geq 1$, and let $D$ be a central division algebra of degree $d$ over $k$. For a positive rational number $r$, write $\operatorname{Mod}_{D,r}$ for the fu…

Let $F$ be an infinite field, and let $A$ and $B$ be central simple algebras over $F$ of the same degree. For each $r<\deg(A)$, write $F_r(A)$ and $F_r(B)$ for the function fields…

Global Azumaya algebra conjecture. There exists a central simple algebra $D$ over $\mathbb Q(\pi)$ such that, for every prime $p$,

Let $K$ be a complete discrete valued field of characteristic $p$ with residue field $k$, and let $A$ be a $p$-algebra over $K$. A maximal subfield of $A$ is totally ramified cycli…

Let $D$ be a central simple algebra and let $G$ and $G'$ be the groups in the Guo–Jacquet comparison, with test functions $f_D=1_{O_D^\times}$ and $f'_D$ as defined from the standa…

Merkurjev–Suslin conjecture. There is an exact sequence

Bayer-Fluckiger et al.'s conjecture. The following statements are equivalent:

Maximality conjecture. The $p^k$-central space $V$ is maximal with respect to inclusion.

Generation conjecture. The algebra $A$ is generated by $X$ and $Y$.

Let $A$ be a central simple algebra over a field $F$, and let ${\mathcal F}_{A,o}$ denote the function field associated with $A$ and orthogonal involutions. An orthogonal involutio…

Universal-element conjecture. All central simple Lie algebras of the same type can be assembled from the same universal elements, which are Lie algebra structures over $\mathbb Z$.

Let $D$ be a division algebra over $F$ and let $E/F$ be a field extension such that $D_E$ remains a division algebra. Consider the Severi–Brauer varieties of $D$ and their motivic…

Let $F$ be a field, let $A$ be a central simple $F$-algebra, and for every extension $L/F$ write $\operatorname{SK}_1(A\otimes_F L)$ for the reduced Whitehead group. Suslin's conje…