2 problems

Let $X$ be a projective hyper-Kähler variety, and let $\mathrm{KS}(X)$ be its associated Kuga–Satake abelian variety. Kuga–Satake motivation conjecture. The variety $X$ is motivate…

Let $X$ be a $K3$ surface over a field of characteristic zero, and let $A$ be the abelian variety associated to $X$ by the Kuga–Satake construction. A Kuga–Satake algebraicity conj…