Cohen–Lenstra heuristics for étale group schemes and symplectic pairings
Cohen–Lenstra heuristics for étale group schemes and symplectic pairings
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用于 étale 群方案和辛配对的 Cohen-Lenstra 启发式
DOI：
10.1112/s0010437x19007036
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发表时间：
2016
影响因子：
1.8
通讯作者：
Jacob Tsimerman
中科院分区：
文献类型：
--
作者：
Michael Lipnowski;Jacob Tsimerman
我们将Cohen – Lenstra启发式方法概括为功能字段，以使用Ellenberg -Venkatesh – Westerland的结果，与恒定组方案相对应的Abelian Groups的经典案例。这些启发式方法。在Malle，Garton，Ellenberg -Venkatesh -Westerland和其他人的作品中，已经建议使用$ \ ell \ ell \ ell \ ell \ ell \ ell $ groups的cohen – lenstra启发式方法。 。
We generalize the Cohen–Lenstra heuristics over function fields to étale group schemes $G$ (with the classical case of abelian groups corresponding to constant group schemes). By using the results of Ellenberg–Venkatesh–Westerland, we make progress towards the proof of these heuristics. Moreover, by keeping track of the image of the Weil-pairing as an element of $\wedge ^{2}G(1)$ , we formulate more refined heuristics which nicely explain the deviation from the usual Cohen–Lenstra heuristics for abelian $\ell$ -groups in cases where $\ell \mid q-1$ ; the nature of this failure was suggested already in the works of Malle, Garton, Ellenberg–Venkatesh–Westerland, and others. On the purely large random matrix side, we provide a natural model which has the correct moments, and we conjecture that these moments uniquely determine a limiting probability measure.