9 problems

Let $\Gamma=SL_2(\mathbb Z)$, let $G_s(z_1,z_2)$ be the Green's function, and let … For a weakly holomorphic modular form $f=\sum_m c_f(m)q^m$ of weight $-2j$, define … For a discr…

Let $Z(W_\mathbb{Q})$ be the CM cycle and let $\Phi^r_L(z,h,f)$ be the higher Green function in the setting of Theorem. Assume that $f$ has integral Fourier coefficients and that t…

Let $(G,X,\Gamma)$ be a real Shimura datum and let $W\subset S_\Gamma$ be an irreducible algebraic subvariety. A CM-point is a point of $S_\Gamma$ at which the Mumford–Tate group o…

Let $Y\subset {\rm Sh}_K^0({\mathbf P},X)$ be a closed irreducible algebraic subvariety of a connected mixed Shimura variety. Classical André–Oort conjecture. If $Y$ contains a Zar…

Equidistribution conjecture. Under the stated finiteness condition, the Galois-orbit measures $\mu_i$ converge weak-$*$ to the uniform probability measure on $X$.

Mixing conjecture. If $\mathfrak{N}_i\to_{i\to\infty}\infty$, then $\mu_i^\mathrm{joint}$ converges weak-$*$ to $\mathrm{m}_Y\times\mathrm{m}_Y$.

Let $N\in\\{1,2,3,4\\}$, and let $z,z'\in\mathfrak H$ be quadratic irrational points satisfying … Assume that $z\notin\varGamma_0(N)z'$, where $\varGamma_0(N)$ is the Hecke congrue…

Let $A_{g,1}$ be the moduli space of principally polarized complex Abelian varieties of dimension $g$. Let $x$ be a CM point in $A_{g,1}$ corresponding to a principally polarized A…

Let $A_{g,1}$ be the coarse moduli space of principally polarized Abelian varieties. A $g$-dimensional Abelian variety $B$ is CM if…