We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic \(p>0\) are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer’s results, implies that varieties of the above type have strongly semistable tangent bundles with respect to every polarization.

中文翻译：

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具有平凡正则丛的普通变体并非不受约束

我们证明了在完美特征域\(p>0\)上的光滑、投影、K平凡、弱普通变体在几何上不是无规则的。我们还展示了我们定理的奇异版本，它在多个方面都很清晰。我们的工作与 Langer 的结果一起表明，上述类型的变体对于每个极化都具有强半稳定的切丛。