52 problems

Let $S\in\mathrm{Rg}$ be a base ring, and let $\mathrm{SH}(S)$ denote the stable motivic homotopy category over $S$. Let $\mathbf{MGL}\in\mathrm{SH}(S)$ be the algebraic cobordism…

Let $D=D_1+\dots+D_n$ be a reduced curve with simple normal crossings on a smooth algebraic surface $V$, and let $\Gamma$ be the dual graph of $D$. For each component, set…

Let $(Y\mid\partial Y)$ be a logarithmic pair, with logarithmic Donaldson–Thomas and stable-pairs generating series, and let the degree-$0$ evaluation denote the degree-$0$ contrib…

Factorization and stability conjecture. There exists a unique $i\in\{1,\ldots,s\}$ such that the Higgs field factors through

Let $D$ be a free divisor in a complex manifold $X$. The logarithmic comparison conjecture. If the logarithmic comparison theorem holds for $D$, then $D$ is strongly Euler homogene…

Let $h$ be a polynomial, let $M_h$ be the coarse quasi-projective moduli scheme of canonically polarized complex manifolds with Hilbert polynomial $h$, and let…

Effective semi-abelian characterization conjecture. There exists an integer $k = k(d) \geq 1$ such that, whenever

Maulik–Ranganathan's conjecture. The generating functions satisfy

Let $(A,M)$ be a log ring, meaning a commutative ring $A$, a commutative monoid $M$, and a map $M\to(A,\cdot)$ of commutative monoids. Let ${\rm THH}(A,M)$ denote its logarithmic t…

Let $M$ be a complex manifold and let $D$ be a reduced free divisor of $M$. An irreducible subvariety $Z$ is weakly log transverse to $D$ when it satisfies the paper's weak log tra…

Let $M$ be a complex manifold, let $D\subset M$ be a free divisor, and suppose that $D$ satisfies the logarithmic comparison theorem. Let $M$ be regarded as the ambient constructib…

Let $M$ be a complex manifold and let $D$ be a reduced free divisor of $M$. A constructible function $\gamma$ is weakly log transverse to $D$ when it satisfies the weak log transve…

Let $S\in\mathrm{Rg}$ be a base ring, let $\mathrm{MS}_{\mathrm{Nis}}(S)$ denote the Nisnevich motivic stable category over $S$, and let $\mathbf{MGL}$ be the algebraic cobordism s…

The paper considers the category of smooth log smooth projective $S$-schemes and seeks a description of the category of resolvable motives using only these schemes. The proposed co…

Let $\overline{\mathcal A}_g$ be the moduli space of stable pairs compactifying the space $\mathcal A_g$ of principally polarized abelian varieties of dimension $g$. A coherent log…

Let $K$ be a complete discrete valuation field extension of $\mathbb{Q}_p$ with perfect residue field, let $\overline{K}$ be an algebraic closure of $K$, and set…

Monodromy-weight conjecture. For every integer $m$, $R^mf_*(\overline{\mathbb{Q}}_{\ell})$ is an object of ${\mathcal A}_Y$ of pure $W$-weight $m$.

Let $(X,D)$ be the logarithmic pair, let $\beta$ be a curve class, and set … Let $\zeta_1,\ldots,\zeta_k$ be cohomology insertions and let $\bm{\mu}(\delta)$ be relative conditions…

Ranganathan–Wise conjecture. The differential $\eta$ is smoothable if and only if, for every level $i$:

Let $S$ be a scheme. Write $\Kthlog(S)$ for its logarithmic $K$-theory spectrum and $\Kth(S)$ for its algebraic $K$-theory spectrum. Logarithmic K-theory comparison conjecture. For…

Let $(X,D)$ be a nef Looijenga pair admitting a deformation to a pair $(X',D')$ with $X'$ toric, $D'_i$ prime toric divisors for $i<l$, and $D'_l$ nef. Let $(Y,L)$ be the correspon…

Let $(X,D)$ be a nef log Calabi–Yau surface pair with $D=D_1+\cdots+D_l$, and let $(Y,L)$ be the associated toric Calabi–Yau threefold with framed Aganagic–Vafa branes…

Let $(X,D)$ be a nef log Calabi–Yau surface pair, with $D=D_1+\cdots+D_l$, and let $d$ be a curve class. Denote by $N_{0,d}^{\rm log}(X,D)$ and $N_{0,d}^{\rm loc}(X,D)$ the genus-z…

Let $\infty_\mathcal{X}$ be a logarithmic target with Gromov--Witten classes, and let $\infty$ be the associated target whose effective classes are under consideration. A class is…

Let $(X,D)$ be an snc Fano pair. For $\vartheta_{p_1},\ldots,\vartheta_{p_r}$ in the $S_X$-module basis of $R_{(X,D)}$, write $\mathbf{p}=(p_1,\ldots,p_k)$, and let…