12 problems

Optimal unitary Drinfeld uniformization conjecture. This isomorphism should be induced by an isomorphism of formal schemes over $\operatorname{Spf} O_K$,

Let $\mathrm{U}(n+1,1)$ be the unitary group considered in the paper, and let $g$ denote the codimension of the special cycles. The paper's main completion and explicit-form statem…

Let $L\subset \mathbb{V}$ be an $O_F$-lattice. The modified derived local density is … where the coefficients $c_{n,i}\in\mathbb{Q}$ are chosen so that…

Let ${\mathcal U}$ and $\mathcal M$ denote the schemes defined in the paper, and consider dimensions $n=5,6,7,8$. Normality conjecture. The scheme ${\mathcal U}$, and hence…

Modularity conjecture. Under the stated assumption, the arithmetic generating series $z(g,\phi)_{{\mathfrak e},{\mathfrak a}}^{\overline{\mathcal L}}$ is holomorphic and modular, w…

Let ${\bm{k}}$ be an imaginary quadratic field, let $V$ be a ${\bm{k}}$-hermitian space of signature $(n-1,1)$, let $\mathcal{S}_V$ be the associated unitary Shimura variety, and l…

Let ${\bm{k}}$ be an imaginary quadratic field, let $V$ be a ${\bm{k}}$-hermitian space of signature $(n-1,1)$, and let $\mathcal{S}_V$ be the associated unitary Shimura variety, e…

Let $E/\mathbb{Q}$ be an imaginary quadratic extension, let $X_K$ be the relevant unitary Shimura variety, and let $Z(T,\varphi)\in \mathrm{CH}^{r(T)}(X_K)$ be the class of the spe…

In the setting of the unitary Shimura varieties $X_{L_{\mathtt{R}}L^{\mathtt{R}}}$ and the codimension-$r$ homologically trivial Chow groups…

Let $E/F$ be a CM extension of number fields, with complex conjugation $\mathtt{c}$, and let $n=2r$ be an even positive integer. Let $W_r=E^n$ with the specified skew-hermitian for…

Vollaard's subscheme conjecture. The subsets $\mathcal{V}(\Lambda)(k)$ are the sets of $k$-valued points of a subscheme of $\mathcal{N}_i$.

Intersection multiplicity formula. The locus $\mathcal Z_{i,j}(\boldsymbol{x})$ is connected and