13 problems

Rapoport–Zink's conjecture. There exists an open subspace

For a local Shimura datum $(G,b,\{\mu\})$, let $\mathcal{F}=\mathcal{F}(G,\{\mu\})$ be the associated flag variety, let $\breve{\mathcal{F}}^{\mathrm{rig}}$ be its rigid analytic b…

Hartl's conjecture.

Hartl's local-system maximality conjecture. The space $\breve{\cal{F}}^0_b$ is the largest open $\breve E$-analytic subspace of $\breve{\cal{F}}^{wa}_b$ carrying a local system…

Let $\mathcal M_4^{(1)}$ be the moduli space under consideration, let $\mathcal M_{\mathrm{Coble4}}^\circ$ be the open locus obtained from smooth stable Coble type quartics, and le…

Let $d4a4_2$, $d4a4_6$, $d4a4_8$, and $d4a4_d$ for $de5 16$ denote the indicated Heegner divisors, and call a Heegner divisor HLS if it has the HLS property used in the paper. HLS…

Banach cohomology and comparison conjecture. There is an isomorphism of topological $K$-vector spaces

Let $\mathrm{ALG}$ and $\mathrm{ALG}^{\ast}$ gravitational instantons be equipped with their period maps, and consider the possible periods arising from their hyperKähler structure…

Let $X$ be a gravitational instanton of type $\mathrm{ALG}$ or $\mathrm{ALG}^{\ast}$, with a fixed diffeomorphism type, and let the cohomology classes of a hyperKähler triple be cl…

Let $(G,[b],\{\mu\})$ be a local Shimura datum with local reflex field $E$, and let $\mathscr{F}\ell_{G,\mu}^{a}\subset\mathscr{F}\ell_{G,\mu}^{wa}$ be the open subspace expected t…

Assume that $F$ has characteristic $0$ and that $\mu$ is minuscule. Let $G$ be the reductive group, let $b_0$ be the basic element associated with $(G,\{\mu\})$, and let…

Assume that $F$ has characteristic $0$, that $mu$ is minuscule, and consider the triple $(G,b,\{\mu\})$. Let ${\mathcal F}^{\rm wa}(G,b,\{\mu\})$ and…

Let $D=G/V$ be a period domain, where $V$ is a compact subgroup of a Lie group $G$, and let $W$ be the $G$-invariant distribution on $D$ inducing a distribution on…