6 problems

Torsion-point conjecture. Each irreducible component of $\Sigma^i_k(X)$ contains a torsion point.

Let $\Gamma$ be a Kähler group, let $X_\Gamma$ be its character variety of homomorphisms $\Gamma\to\mathbb{C}^*$, and let … An isolated point of $X^1_\Gamma$ is an isolated charact…

Let $X$ be a smooth algebraic variety, and let $\mathcal F$ be a semisimple perverse sheaf on $X$. An absolute $\overline{\mathbb Q}$-point is a complex perverse sheaf satisfying t…

Let $X=\mathbb{C}^n$, let $f:X\to\mathbb{C}$ be holomorphic, let $x\in f^{-1}(0)$, and for a sufficiently small ball $B_x$ centered at $x$ set … Thus $U_{f,x}$ is the complement of…

Let $X$ be the complement of a hyperplane arrangement, and let $\Sigma^i_k$ denote its cohomology jump loci of rank-one local systems. The intersection lattice of the arrangement i…

Cone conjecture. Under this isomorphism, $S_{(\rho)}$ must be a cone in $C_{(0)}$.