We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H^c_I (R)$ is faithful, where $c$ is the cohomological dimension of $I$. In particular, we prove that this is true for the case of positive prime characteristic when $c$ is the number of generators of $I$.

中文翻译：

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领域中顶级本地同构模块的真实性

我们研究的条件是，在理想$ I $的支持下，域$ R $的最高不消失局部同调模块对$ R $的忠实度，即保证$ H ^ c_I（R）$的忠实度，其中$ c $是$ I $的同调维度。特别地，我们证明当$ c $是$ I $的生成器数时，对于正质数特征的情况是正确的。