32 problems

Let $f^\circ:X^\circ\to S^\circ$ be a smooth family of canonically polarized varieties. The family has maximal variation when its variation equals the dimension of the base. Viehwe…

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…

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 $M$ 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…

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…

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 $X$ be a smooth space in the setting of the paper, and consider the projective maps … Let $M$ be a corresponding $Z$-projective differential crystal spectrum. Logarithmic cryst…

Kummer pro-étale extension conjecture. The construction developed in the section should extend to suitable Kummer pro-étale sites with logarithmic perfectoid subdomains forming a b…

Logarithmic Kummer Poincaré conjecture. The logarithmic versions of the strictly exact long exact sequences in the Poincaré lemma for the rigid-analytic situation should hold for t…

Let $(X,D)$ be a logarithmic pair, let $\beta$ be a curve class, let $\mu$ be a relative insertion, and let $\tau_{k_i}(\gamma_i)$ be descendent insertions. Denote the logarithmic…

Let $f\colon (U,D)\to V$ be a log smooth family with $V$ quasi-projective, with all coefficients of $D$ in $(0,1)$, and suppose that every fiber $(U_y,D_y)$ is of log general type.…

Let $f_U:U\to V$ be a smooth family of projective varieties, and let $(X,D)$ be a smooth compactification of $V$ with $V\cong X\smallsetminus D$. Assume that the geometric general…

Logarithmic bend-and-break conjecture. Through a general point of $C$ there is a rational curve meeting $D$ at most once.

Let $X$ be a compact Kähler manifold and let $D=\sum_{i=1}^r D_i$ be a simple normal crossing divisor in $X$. Let $L$ be a holomorphic bundle over $X$ such that … where…