4 problems

Shapiro's conjecture. $(A,\sigma)$ admits a decomposition as a tensor product of $r$ quaternion algebras with involution in which each quaternion algebra is split.

Let $\alpha\geq 1$ be a real number. An algebra with involution $A_\alpha$ has a $*$-PI-exponent, when the limit exists, defined by … Realization conjecture for $*$-PI-exponents. F…

Let $A$ be a finite-dimensional algebra with involution $*\colon A\to A$. Its $*$-codimensions are denoted by $c_n^*(A)$, and when the limit exists its $*$-PI-exponent is … Existen…

Pfister involution conjecture.