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Distributions of modules over finite local $\mathbb{Z}_p$-algebras Klys, Jack


Recently Lipnowski and Tsimerman defined a 'Cohen-Lenstra' type measure on $R$-modules for certain rings $R$, and by extending methods of Ellenberg-Venkatesh-Westerland proved that moments of the Picard group of hyperelliptic curves (viewed as a module over the Frobenius) 'almost' converge to the moments of this measure. Under certain conditions on the ring $R$ knowledge of these moments can determine a distribution. We study when such conditions occur, as well as other questions related to the above measure.

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