5 problems

General Hodge conjecture. This embedding is fully faithful.

Let $E_7$ be an elliptic curve with complex multiplication by $\mathbb{Q}(\sqrt{-21})$, and let … be a fiber of the hypergeometric family. The $(2,3,7)$ Hodge-structure conjecture.…

Let $\mathcal{A}$ be a smooth proper triangulated category. The Hochschild homology (or rather the cyclic homology) of $\mathcal{A}$ should be endowed with a Hodge structure. This…

A two-dimensional Hodge structure of odd weight is a Hodge structure of odd weight and underlying rational vector space of dimension two; here, a Hodge structure is associated to a…

Let $X$ be a smooth projective variety of dimension $n$, let $k\leq n$, and let $H'$ be a sub-Hodge structure of $H^k(X,\mathbb{Q})$ with no component of type $(k,0)$. Generalized…