19 problems

Let $X$ be a closed subscheme of a smooth scheme over a perfect field $k$, and let $\mathcal{F}$ be a constructible complex of $\Lambda$-modules of finite Tor-amplitude on $X$. Let…

Kazhdan–Lusztig irreducibility conjecture. In type A, the characteristic cycle of the IC-sheaf $\mathcal{L}_Q$ is irreducible.

Let $f:X\to S$ be universally $M$-transversal for a motive $M\in\mathbf{T}_c(X)$, and let $C_{X/S}(M)\in H_0(X/S)$ be its relative characteristic class. Relative characteristic-cyc…

Let ${\mathscr F}$ be a constructible étale sheaf of flat $\Lambda$-modules on $\eta$, and let $r>1$ be a critical slope of ${\mathscr F}$. Assume that … Thus $r$ is the unique cri…

Let $(V,0)\subset(\mathbb{C}^n,0)$ be a complex analytic germ, let $W$ be a local ambient representation, and let $\tilde{\nu}$ be a continuous vector field on $W$ with an isolated…

Microlocal multiplicity conjecture. For every loopless matroid $M$,

Let $k$ be a perfect field, let $X$ be a smooth scheme over $k$, let $\mathcal F\in D_{\rm ctf}(X,\Lambda)$, and let $SS(\mathcal F)$ be its singular support. Let $Z\subseteq X$ be…

Suppose that $X$ is purely of dimension $d$ and that $D$ has simple normal crossings. Let $I'subset I$ be a subset containing $I_{\mathrm{T},\mathcal{F}}$, and let … Assume that th…

Characteristic-cycle conjecture. One has

Let $X$ be an aspherical complex projective manifold. A constructible function on $X$ has an effective characteristic cycle when its characteristic cycle is effective. Uniform non-…

Let $G$ be the reductive group in the construction, with Borel subgroup $B$ and parabolic subgroup $P$, and let $\mathscr W$ be its Weyl group. For $w\in\mathscr W$, let $w^{\max}$…

Let $f\colon X\to Y$ be a proper morphism of smooth schemes over a perfect field $K$, with $X$ of dimension $n$ and $Y$ of dimension $m$, and let $\mathcal F$ be a constructible co…

Let $(I,Q)$ be a type $A$ quiver with orientation $i\rightarrow i+1$, let $V$ be an $I$-graded vector space, and let $S$ and $S'$ be $G_V$-orbits in the representation variety…

Let $X$ be a scheme and let $\mathbf{T}_c(X)$ be the relevant triangulated category of constructible motives. The additivity of characteristic classes gives a homomorphism … where…

Let $k$ be a perfect field, and let $f\colon X\to Y$ be a morphism of smooth schemes over $k$. Assume that every irreducible component of $X$ has dimension $n$ and every irreducibl…

Characteristic-cycle push-forward conjecture. We have

Let $Q$ be a quiver without loops, let $\lambda$ be a parameter, and let $\mathcal{A}_\lambda(v)$ be the corresponding quantized quiver-variety algebra. Let $\mathsf{CC}^\lambda$ b…

Let $X$ be a smooth scheme over $k$, let $D$ be a divisor with simple normal crossings, and let $U=X\setminus D$. Let ${\cal F}$ be a locally constant sheaf of free $\Lambda$-modul…

Higher-dimensional equivalence conjecture. Motivated by the calculations in dimensions $n=2,3$ and $4$, the same three conditions should be equivalent for all higher dimensions…