4 problems

Regularity conjecture. The module $\mathcal{M}$ is regular holonomic if and only if $Sol^t(\mathcal{M})$ is regular. The text notes that the only-if direction follows from the prec…

Real-constructibility conjecture. The ind-sheaf $Sol^t(\mathcal{M})$ belongs to $D^b_{\mathbb{R}\text{-c}}(\mathrm{I}[\mathbb{C}_X])$. This is presented as a consequence of the pap…

Let $X$ be a real analytic manifold, let $F\in D^b_{{\rm w-}\mathbb{R}\text{-c}}(\mathrm{I}[k_X])$, and let $G\in D^b_{{\rm w-}\mathbb{R}\text{-c}}(k_X)$. Closure conjecture. The o…

Let $X$ be a complex analytic manifold and let $\boldsymbol{P}$ denote the complex projective line. Consider the contravariant functors … obtained from tempered holomorphic solutio…