10 problems

Let $K$ be a discretely valued field with separable closure $K^{\operatorname{sep}}$, let $X$ be a variety over $K$ with semistable model, and let $E_r^{p,q}$ be its weight spectra…

Kato's log $l$-adic monodromy-weight conjecture. If $\overset{\circ}{X}$ is projective over $\kappa$, then, for every $e\in{\mathbb Z}_{\geq 1}$, $N$ induces an isomorphism

Let $\Psi$ be the nearby-cycle object with filtrations $F$ and $G$, let $\mathbb{D}$ denote duality, and let $b$ be the isomorphism relating the dual nearby cycles to…

Let $C$ be a complex integral projective curve whose normalization has genus zero and whose unique planar singularity is locally given by $f(x,y)=0$. Let…

Let $L_{10}=P_{10,425}$ and let $\mathcal{W}_{12}$ denote the weight-12 component. $L_{10}$ weight decomposition conjecture. The period $L_{10}$ mixes weights $12$ through $14$, an…

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and $c_2(G)=0$. Suppose $P(G)$ is mixed Tate. Refined weight-mixing conjecture. Either $P(G)$ has pure we…

Weight bound conjecture. The amplitude integrand satisfies

Let $X$ be a smooth quasi-projective variety over $\overline{\mathbb Q}$, and let $j$ and $k$ be integers. Let $H^k_{\rm dRB}(X,\mathbb Q(j))_{\rm Gr}$ denote the Grothendieck clas…

Let $X$ be regular, let $W_0$ be the sum of generalized $\phi$-eigenspaces whose eigenvalues are roots of unity, and let $\operatorname{sp}$ be the étale specialization map. Weight…

Let $X$ be regular, and let $W_{i-1}$ denote the indicated weight filtration on the $p$-adic étale cohomology groups of the special and geometric generic fibres. Let…