Building on work of Segre and Kollár on cubic hypersurfaces, we construct over imperfect fields of characteristic $p\geq 3$ particular hypersurfaces of degree p, which show that geometrically rational schemes that are regular and whose rational points are Zariski dense are not necessarily unirational. A likewise behavior holds for certain cubic surfaces in characteristic $p=2$ .

中文翻译：

---

正特征超曲面的不合理性和几何不合理性

在 Segre 和 Kollár 在三次超曲面上的工作的基础上，我们构建了特征 $p\geq 3$ 特定p次超曲面的不完美场，这表明规则且其有理点为 Zariski 密集的几何有理方案不一定是非有理方案. 同样的行为适用于特征 $p=2$ 中的某些立方曲面。