6 problems

Mod-$p$ vanishing conjecture. Assume $p$ is chosen so that holds. Then

Relative Etingof–Lee $p$-curvature conjecture. The connection satisfies

Canonical splitting conjecture. Given these idempotents, the space $H^*(M)[q^{\pm 1}][[t]]$ carries a canonical splitting into graded $R[q^{\pm 1}][[t]]$-modules, invariant under…

Let $(X,comega)$ be a closed monotone symplectic manifold of dimension $2n$, with $[comega]=c_1(X)$. Let $t$ be a formal variable of degree $2$, and let … be the quantum $t$-connec…

Exponential-type conjecture. The quantum $t$-connection has a decomposition into connections with simple poles at $0$ and monodromy being roots of unity; equivalently, it has expon…

Quantum-connection conjecture. (i) $\nabla_{\partial_q}$ has a singularity of unramified exponential type at $q=\infty$. (ii) The regularized formal monodromies at $q=\infty$ are q…