18 problems

Conjecture 5.3.5. For the case $g=3$, $\mathfrak i=2$, any $\sigma_1,\sigma_2\in\mathfrak D_1\cap S(3,2)^{open}$ satisfy 4.2.6.

Conjecture 4.2.20. There exists $i\in\{1,2\}$ such that the parts of the $I$-partition restricted to $S(3,1)_{D(\sigma)}$ coincide with the fibers of $\pi_{\sigma,i}$. In particula…

Conjecture 1.6.3. The $D$-partition of $S(g,\mathfrak i)$ is a subpartition of the $\mathfrak D$-partition.

Conjecture 1.5.7. The action of $\operatorname{Gal}(K^p/K^1)=\mathbb F_{p^2}^*/\mathbb F_p^*$ on the set of parts of the $I$-partition contained in any fixed part of the $D$-partit…

Conjecture 1.5.6. The restriction of the $I$-partition to $\goth D_{2g}$ is the intersection of the $\goth H$-partition with the restriction of the $D$-partition to $\goth D_{2g}$.

Conjecture 1.5.4. The $D$-partition of $S(g)$ is a subpartition of its $\goth D$-partition. Two elements $\sigma_i,\sigma_j\in\goth D_j$ are $D$-equivalent if and only if the quadr…

Let $S^*_{g,i}(j,k)$ be the stratum indexed by $(j,k)$, let $S'_{g,i}(l)$ be a component of the Hecke parameter space, and let $\pi'^*_{i;j,k;l}$ be the restricted projection to…

Let $\Psi_{j,k}(V)$ be the conjectural subvarieties associated with the compositions $\Phi_j\circ\Phi_k$ for a non-ordinary point, and let $W,W_1,W_2$ be the corresponding isotropi…

Let $\pi_{i;j,k}:S_{g,i}(j,k)\to G(j,k,g)(\mathbb{Z}/p^2)$ be the natural projection sending an isotropic subspace to its intersection with the Frobenius kernel, and let…

Let $\mathfrak V$ be a subvariety whose generic point has ordinary reduction at $p$, and let $\tilde{\mathfrak y}$ be the Abel–Jacobi image of its reduction. Let…

In the Section 5 setting, let $M$ be the integer used in the divisibility argument, and let $\alpha_{p,j_*}$ be the multiplicities of bad components. The source singles out…

Consider the $p$-Hecke correspondence $T_{p,1}$ in the setting of Section 5, and let $L_{{good}}$ index its good components with multiplicities $\alpha_{p,i_k}$. Conjecture 5.0. Al…

Let $S^*_{g}(j)$ and $S'_{g}(l)$ be the partitions of the relevant Hecke parameter space, and let $\pi'^*_{j,l}:S^*_{g}(j)\cap S'_g(l)\to G(j,g-1)$ be the restricted projection. As…

Let $V_l$ be a component in the decomposition of a Hecke correspondence, let $\tilde{\mathfrak z}_l$ be the Abel–Jacobi image of its reduction, and let $\tilde y_1$ be the reduced…

Let $t\neq t'$ and let $A$ be any closed formal subscheme of the Rapoport–Zink space $\mathcal{N}_n$. The correspondence $\mathcal{T}_n^{\leq t}$ is obtained by composing the corre…

Let $C$ be the underlying curve, let $c\in C$, and let $W^+_0$ and $W^+_c$ be the upward flows from the canonical fixed point and from the fixed point indexed by $c$, respectively.…

Let $S$ be the smooth projective surface and let $\CM$ denote the relevant smooth moduli space of sheaves. For each $n\in\BN$, write $e_{(0,...,0)}$ for the functor associated with…

In the Shimura-datum setup, let $S_{\mathbf H,\gamma}$ be the special subvariety associated with $\gamma\in\Omega\subset\mathbf G(\mathbb Q)_+$ and let $N(\gamma)$ be the complexit…