5 problems

Realization and compatibility conjecture. The following assertions hold:

Let $M$ be a hypergeometric motive, let $p$ be a prime, and let $k=\operatorname{ord}_p(t)$. Let $F_p(M,x)$ be the Frobenius polynomial and let $f_p(M,x)$ be the factor obtained by…

Let $M$ be a hypergeometric motive, let $p$ be a prime, write $t=vp^k$ with $k=\operatorname{ord}_p(t)$, let $c_p=\operatorname{ord}_p(\operatorname{Conductor}(H([-8,3,5],t)))$, le…

Let $\#n$ be a row in Table 1 with $n\ne7,13,14,15,16$. Let $f$ be the Hilbert cusp form associated with that row, let $F$ be its real quadratic field, let $\psi$ be the central ch…

Let $\boldsymbol\alpha$ be a set of parameters from Table 1 and let $\boldsymbol\beta=\{1,1,1,1,1\}$. For a hypergeometric motive $H(\boldsymbol\alpha,\boldsymbol\beta\mid z)$, wri…