5 problems

Modularity conjecture. The function

Arithmetic modularity conjecture. The function $\widehat{\phi}_\kappa$ is a cusp form. For $\kappa=1$, the source states that arithmetic modularity on the modular curve $X_0(N)$ ha…

Let $\mathrm{Pin}^{\mathrm{alg}}$ be the subgroup of algebraic principal cycles and let $\mathrm{Pin}$ be the subgroup of principal cycles in the group of Heegner cycles. Principal…

Let $G\in S_{2\kappa}^{new}(N)$ be a normalized newform, let $F_G$ be the totally real field generated by its eigenvalues, and let…

Let $(f,K,\mathfrak p)$ be an admissible triple. Let $K_\infty$ be the anticyclotomic $\mathds Z_p$-extension of $K$, let $\Lambda={\mathcal O}_\mathfrak p[[\Gamma_\infty]]$ be its…