10 problems

Let $X$ be a smooth projective variety defined over a finitely generated subfield $F\subset\mathbb{C}$. Under the Artin comparison identification … let…

Let $X$ be a hyper-Kähler variety, and let $\mathfrak{h}(X)$ denote its motive. For each degree $i$ and prime $ell$, let $\mathbf{G}_{\ell,i}(X)$ be the $ell$-adic algebraic monodr…

Let $S$ be the base of the family considered in the paper. A special subvariety is a closed irreducible complex subvariety maximal among those having a fixed generic Mumford–Tate g…

Let $S$ be the base of the family considered in the paper, and for a subvariety $Z\subset S$ let $G_Z$ and $G_Z^{AH}$ be its generic Mumford–Tate and generic absolute Mumford–Tate…

Let $X$ be a smooth projective variety over $K$, let $G_X^{AH}$ denote its absolute Mumford–Tate group, and let $G_{\ell,X}$ denote its $\ell$-adic algebraic Galois group. Absolute…

Let $B$ be an abelian variety over a number field $L$, let $C=\operatorname{Spec}(L)$, and let … be the continuous representation describing the action of the absolute Galois group…

Let $X$ be as above, let $H$ be the Mumford–Tate group, and let $H^{\operatorname{sc}}$ be the simply connected cover of its derived group. Let…

Let $X$ be a nonsingular projective variety over a number field $K$, let $i$ be a non-negative integer, and let $V_\ell=H^i(\bar X,\mathbb{Q}_\ell)$, where $\bar X=X\times_K\bar K$…

Let $A/K$ be an abelian variety of dimension $g$ over a number field, of type $\operatorname{GSp}$. Let … be the associated … -adic monodromy groups. The source presents it as the…

Let $A$ be an abelian variety over a number field, and let $\gamma(A)$ be the infimum of the real numbers $x>0$ such that, for every finite extension $F/K$, one has…