In the present paper, we study the Bethe ansatz equations for Gaudin model and Miura opers in characteristic . Our study is based on a work by E. Frenkel, in which solutions to the Bethe ansatz equations are described in terms of Miura opers on the complex projective line. The main result of the present paper provides a positive characteristic analogue of this description. We pay particular attention to the case of Miura -opers because dormant generic Miura -opers correspond bijectively to Tango structures, which bring various sorts of pathological phenomena in positive characteristic, e.g., counter-examples to the Kodaira vanishing theorem. As a consequence, we construct new examples of Tango structures by means of solutions to the Bethe ansatz equations modulo .

中文翻译：

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Gaudin 模型模 p、Tango 结构和休眠的 Miura 操作符

在本文中，我们研究了 Gaudin 模型和 Miura 算子的 Bethe ansatz 方程的特征 。我们的研究基于 E. Frenkel 的一项工作，其中 Bethe ansatz 方程的解是用复射影线上的 Miura 算子来描述的。本文的主要结果提供了这种描述的积极特征类比。我们特别关注Miura -opers的情况，因为休眠的通用Miura -opers双射对应于Tango结构，它带来了积极特征的各种病态现象，例如小平消失定理的反例。因此，我们通过 Bethe ansatz 方程模 的解来构建 Tango 结构的新例子。