15 problems

Let $Z^{\mathrm{sym}}_{N,r}$ be the symmetric Hilbert modular surface, and consider each $(N,r)$ in parts (ii)–(iii) of the paper's classification theorem. A Jacobian elliptic fibr…

Let $F$ be the real quadratic field and let $K$ be a CM extension of $F$ as in the preceding construction. Write $\mathcal{O}_F$ for the ring of integers of $F$, let $\mathfrak l$…

Let $K=\mathbb Q(\sqrt D)$, let $I$ be a level, and let $f$ be a Hilbert cuspidal newform of level $I$ over $K$. Suppose there exist a quadratic field $\mathbb Q(\sqrt n)$ and a qu…

Let $H_{I,K}$ and $K_E=(E\times E^\sigma)/\pm1$ be as in the Oda-Hamahata conjecture, and let the conjectured correspondence be defined over an algebraic closure…

Let $K$ be a real quadratic field, let $I$ be an ideal of ${\mathcal O}_K$, and let $H_{I,K}$ be the Baily–Borel compactification of the Hilbert modular surface of level $I$. For a…

Let $N$ be an integer coprime to $6$, let $r$ be as in the construction, and let $Z^\circ_{N,r}$ and $W_{N,r}^{\mathsf{small}}$ be the models defined in the nonsingular-model and g…

Let $N$ be an integer coprime to $6$, let $r$ be as in the construction, and let $Z^\circ_{N,r}$ and $W_{N,r}^{\mathsf{small}}$ be the nonsingular and closer-to-minimal models defi…

Let $Z^{\mathrm{sym}}_{N,r}$ denote the symmetric Hilbert modular surface associated with an $(N,r)$-congruence, and suppose $(N,r)$ is one of the pairs in part (i) of the paper's…

Let $F$ be a real quadratic field, let $E/F$ be a modular elliptic curve with everywhere good reduction, and let $K/F$ be an almost totally real quadratic extension. With the assoc…

Integral lifting conjecture. The resulting action of $U_f^\vee\otimes k$ on the special fiber lifts to an integral action of $U_f^\vee$.

Let $Y$ be the canonical smooth model of an irrational Hilbert modular surface, and consider the curves on $Y$ arising as modular curves or from the desingularization. Hirzebruch–Z…

Unramifiedness and nilpotent ramification conjecture. The representation $\bar\rho$ is unramified at $\mathfrak{p}$, and there exists a positive integer $n$ depending on $g$ such t…

Let $K$ be the real quadratic field in the paper, let $\rho$ range over the resolution curves of the cusps of the Hilbert modular surface $Y_{cGamma({\mathscr{O}}_K,\id{a})}$, and…

Bruinier–Yang conjecture. The arithmetic intersection satisfies

Let $F$ be a real quadratic field, let $K=F(\sqrt{\Delta})$ be a quartic non-biquadratic CM field, and let $\mathcal M$ be the moduli stack of principally polarized abelian surface…