4 problems

Let $\pi$ be as in the $p$-adic cohomological setting, let $\text{\dn{v}}_{\pi,p}$ be the $p$-adic motivic cohomology space, and let…

Let $G$ be a reductive group over $\mathbf{Q}$, let $\pi_f$ be a finite part of a cohomological cuspidal automorphic representation, and let $E(\pi_f)$ be a number field over which…

Let $Y(K)$ be the arithmetic manifold, let $E$ be the coefficient field, and let $M_{\mathrm{coad}}$ be the coadjoint motive with its integral model $(M_{\mathrm{coad}})_\mathbb Z$…

Let $K$ be the level, let $\mathfrak m$ be the maximal ideal associated to $\pi$, and let … with $f\in H^*(Y(K),E)_\mathfrak m$. Galatius--Venkatesh compatibility conjecture. The d…