MathOverflow

Fix an integer $s\ge 1$. Let $n=m_1+\dots+m_r$ be a partition of $n$ into parts $m_i\ge s+1$, and let $k_j$ be the number of parts equal to $j$. I want to know whether$$\Big(\prod_{i=1}^r (m_i-s)\Big)\Big(\prod_j k_j!\Big)\ \Big|\ (n-1)!\qquad(\star...

Let $A/\mathbb{F}_p$ be an abelian variety. Proposition 3(1) in Section 3 of this paper by Howe and Zhu states the following:
If $\mathbb{Q}(\pi^d)=\mathbb{Q}(\pi)$ for all $d>0$, then $A$ isabsolutely simple. If $A$ is ordinary, then the converse also holds....

Some evidence suggests that there was a conference titled Colloque pour le centenaire d’André Weil held at IHES in 2006, but the official conference website does not exist anymore. Also I have been unable to find any complete related information online...

The matrices I am dealing with are $n\times n$ of the following type (with $n=7$):
$M_7=\begin{pmatrix}1&0&0&0&0&0&1 \\ 1&1&0&0&0&0&0 \\ 0&1&1&0&0&0&0 \\ 0&0&1&1&0&0&0 \\ 0&0&0&1&1&0&0 \\ 0&0&0&0&...