6 problems

Let $\mathcal A$ be the set of cuspidal automorphic representations defined above. For $\pi\in\mathcal A$, let … where $S$ ranges over the relevant finite sets and…

Let $CM$ be the module over the full Hecke algebra generated by a CM cycle on a Kuga–Sato variety, and let $\overline{CM}$ be its quotient by the kernel of the Beilinson–Bloch heig…

Bruinier–Yang conjecture. The arithmetic intersection satisfies

Let $\omega$ be the integral modular line bundle equipped with the Petersson metric, let $\hat{\omega}$ denote the resulting metrized line bundle, and let $\mathcal{Z}(U)$ be the C…

Let $f\in H_{1-n/2, \bar{\rho}_L}$, let $c^+(0,0)$ be its constant term, let $\hat{\mathcal{Z}}(f)$ be the associated arithmetic divisor, and let $\kappa(0,0)$ be the constant coef…

Let $L$ be the relevant lattice, let $U$ be the negative-definite subspace defining the CM cycle, and let $P$ and $N$ be the positive- and negative-definite lattices arising from a…