10 problems

Let $f:X\to\mathbf A^1$ be a function on a smooth complex algebraic variety, and let $x$ be a closed point of $f^{-1}(0)$. Suppose the singular locus of $f$ is a curve with local c…

Let $\pi:\mathcal X\to\Delta$ be a projective conifold degeneration, and let $\mathcal P$ be the corrected perverse object constructed from nearby and vanishing cycles. Suppose the…

Let $\pi:\mathcal X\to\Delta$ be a projective conifold degeneration, and let $\mathcal P$ be the corrected perverse object constructed from nearby and vanishing cycles. A mixed-Hod…

Let $X$ be the underlying space, let $\mathcal{M}$ be a regular holonomic $\mathscr{D}_X$-module, and let $\mathcal{N}_0$ be the associated module. For a monoid ideal…

BPS complex conjectures. The following assertions should hold:

Let $X$ be an algebraic variety over $\mathbb{Q}$. An object $M$ of the abelian category $\mathcal{M}_\mathrm{univ}(X,\mathbb{Z})$ is torsion-free if multiplication by every nonzer…

Let $X$ be a compact Kähler or complex projective manifold that is aspherical or has a nef cotangent bundle, and let $\mathcal{M}$ be a mixed Hodge module on $X$. For an integer…

Let $X$ be a complex projective manifold, let $\mathbb{M}$ be a Mixed Hodge Module on $X$, and let $H^k_2(\widetilde{X},\mathbb{M})$ denote the associated $L_2$ cohomology, equippe…

Let $cM$ be a regular holonomic $cD_X$-module, and let $W\to X$ be a relative compact open subset. Suppose that, locally on $W$, … for some $n\le l\le n+r$. For a support locus…

Let $Q_L^n$ be the Quot schemes associated with the local line $L\subset\mathbb A^3$, and let…