12 problems

Top-codimension conjecture. For all $g\geq 1$,

Algebraic homomorphism conjecture. The homomorphism property holds for all classes $d6fc,d6fd\in\mathsf{CH}^*(\mathcal{A}_g)$ defined over $d53e$.

Zeta-extension conjecture. The mixed Hodge structure on $H^{2g}_c(\mathcal{A}_g)$ has a subquotient isomorphic to such an extension whose class is given by a nonzero rational multi…

Tensor-algebra injectivity conjecture. This induced map is injective. The later sections provide various kinds of evidence for this conjecture, while the equivalent formulation in…

Let $k$ be a field of characteristic $p>0$, let $E$ be a supersingular elliptic curve over $k$, and for $g\geq 2$ let $\mathcal{A}_g$ denote the moduli space of principally polariz…

Nef-cone conjecture. The cone of nef codimension-two classes is

Let … lambda{2i+1}$and the classes of boundary strata, and no polynomial in the$Dm$, is identically zero for$g$ sufficiently large. This predicts algebraic independence of the i…

Let $\overline{\mathcal{A}}_5$ be a compactification of the moduli space of principally polarized abelian fivefolds, and let $s'(\overline{\mathcal{A}}_5)$ denote its moving slope.…

$\Gamma_{00}$ conjecture. If

Theta-multiplicity conjecture.

Debarre's codimension conjecture. For any $1\leq k\leq g-3$,

Vanishing conjecture. The intersection numbers $a_N^{(g)}$ for any $N$ vanish unless $G-N=k(k+1)/2$ for some $k\le g$. The claim extends the vanishing pattern established in the pa…