4 problems

Let $L$ be a lattice of signature $(n,2)$, let $X$ be the associated orthogonal Shimura variety, and for $1\leq g\leq n$ let $\mathcal Z(M)$ be the codimension-$g$ special cycle as…

Let $M_K$ be the orthogonal Shimura variety, let $e>1$, let $r$ be a positive integer, and let $\phi_f\in S(V^r(\mathbb{A}_f))^K$. For…

Let $(V,Q)$ be a quadratic space over a local non-archimedean field $F$ with $\epsilon(V)=-1$ and unit determinant, and let $K=F(\sqrt{D})$ be the unramified quadratic extension of…

Let $V^{\prime}=V^{\Phi}_{K_{0}}$ be the nearby quadratic space, let $\breve{\mathcal{M}}_{\mathrm{red}}$ be the reduced special fiber, and let $\breve{\mathcal{M}}_{\mathrm{ssp}}$…