We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have very large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.

中文翻译：

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Fano超曲面的扭转阶数

我们在任意特征的（不可数）场上的非常普通的Fano超曲面的扭转阶数上找到了新的下界。我们的结果表明，大多数Fano超曲面的非理性参数化必须具有非常大的程度。我们的结果也存在于特征二中，它们解决了对数度界下超曲面的合理性问题，从而将作者先前的结果从不同于二的特征扩展到任意特征。