Distribution of cokernels of ($n$+$u$) $\times$ $n$ matrices over $\mathbb{Z}_p$

Ling-Sang Tse

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arXiv · 1608.01714

Distribution of cokernels of ($n$+$u$) $\times$ $n$ matrices over $\mathbb{Z}_p$

Ling-Sang Tse

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Abstract

Let $n, u \geq 0$, $M$ be a ($n$+$u$) $\times$ $n$ matrices over $\mathbb{Z}_p$, and $G$ be a finite abelian p-group group. We find that the probability that the cokernel of $M$ is isomorphic to $\mathbb{Z}_p^u \oplus G$ as $n$ goes to infinity is exactly what is expected from Cohen-Lenstra heuristics for the classical case when $u$ is negative.

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BibTeX RIS

Ling-Sang Tse. 2016-08-04. Distribution of cokernels of ($n$+$u$) $\times$ $n$ matrices over $\mathbb{Z}_p$. https://arxiv.org/abs/1608.01714

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