We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic $𝒟$-modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties, and a criterion for the simplicity of the arising Lie algebras.

中文翻译：

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高斯图谱的特征周期和微局部几何，II

我们证明了半简单完整的Tannakian群的权重的任何Weyl群轨道 $𝒟$通过切切束上的拉格朗日循环，可以实现阿贝尔变体上的模数模块。在应用中，我们讨论了第五类中对肖特基问题的弱解，对阿贝尔变体上亚变数和的存在性的阻碍以及对所产生的李代数的简单性的判据。