4 problems

Let $\tilde{{\mathcal{K}}}$ be the maximal anticyclotomic ${\mathbf{Z}}_p^d$-extension of a CM field ${\mathcal{K}}$ with Galois group $W$, and put…

Matar's conjecture. The module $Y(E/F^{\mathrm{ac}})$ is finitely generated over $\mathbb{Z}_p$.

Let $A/{\mathbb Q}$ be an abelian surface associated with a Siegel cusp form $f$, let $K$ be an imaginary quadratic field, and let $K^-_\infty/K$ be the anticyclotomic…

Let $K$ be a finite extension of the imaginary quadratic field $k$ contained in $k^{\operatorname{cyc}}$, let $F$ be its maximal totally real subfield, and let ${\bf f}$ be the Hil…