5 problems

Let $B^{\vee,+}$ and $B^{\vee,-}$ be opposite Borel subgroups of $G^{\vee}$ with $B^{\vee,+}\cap B^{\vee,-}=T^{\vee}$. Set $\mathcal{W}=B^{\vee,-}B^{\vee,+}\subset G^{\vee}$, let…

Hodge decomposition conjecture.

Hodge lift conjecture. For any complex Lagrangian $L$, the object

Microsheaf wrapping conjecture. There exists an inductive system $\{\mathcal E_i\}$ in $\mu\operatorname{sh}_{\mathbb C\text{-}c}(X)$ such that

Cotangent-fiber Hodge microsheaf conjecture. Hain's Hodge structure is induced by a Hodge microsheaf whose underlying microsheaf corresponds to a cotangent fiber.