Generalizations of results of Friedman and Washington on cokernels of random $p$-adic matrices

Gilyoung Cheong, Nathan Kaplan

Let $p$ be prime and $X$ be a Haar-random $n\times n$ matrix over ${\mathbb{Z}}_p$, the ring of $p$-adic integers. Let $P_1(t),\dots ,P_l(t)\in {\mathbb{Z}}_p[t]$ be monic p…