7 problems

Let $\mathfrak p$ and $\mathfrak p'$ be parabolic subalgebras defining parabolic categories $\mathcal{O}_0(\mathfrak{sl}_n)^{\mathfrak p}$ and…

Finiteness conjecture. There exist only finitely many isomorphism classes of endomorphism algebras of these abelian varieties.

Let $A$ be an abelian variety of dimension $g\geq 1$ defined over a number field $k$ of degree $d$. Write $A_{\overline{\mathbb Q}}$ for its base change to $\overline{\mathbb Q}$,…

Let $X$ be an absolutely simple abelian variety over a number field $F$. After replacing $F$ by a finite extension if necessary, let $d^2$ be the dimension over its center of the d…

Endomorphism-algebra factorization conjecture. This natural map is an isomorphism. The claim says that, after adjoining closed diagrams from the identity endomorphism algebra, all…

Injectivity conjecture. The natural map is injective. This conjecture identifies the explicitly presented algebra $H_i^n$ with a subalgebra of the endomorphism algebra; the source…

Assume $\mathbb F$ is algebraically closed. Let $V$ be a vector space over $\mathbb F$ with finite positive dimension, and let $A,A^*$ be a tridiagonal pair on $V$. The involutive…