A variety $ X $ is $ F $-split if there exists an $ \mathcal{O}_{X} $-linear map $ \phi: F_{\ast}(\mathcal{O}_{X}) \to \mathcal{O}_{X} $ such that $ \phi \circ F^{\sharp} = \operatorname{id}_{\mathcal{O}_{X}} $. Such a map $ \phi $ is called a splitting. A closed sub-scheme $ Y $ of $ X $ is co...

Let us denote the Frobenius endomorphism of a variety $ X $ by $ F $. A variety $ X $ over a field $ k $ of positive characteristic is globally $ F $-regular if for every effective Weil divisor $ D $, there is an $ e \in \mathbb{N}_{0} $ such that the morphism $ \mathcal{O}_{X} \to F^{e}_{\ast}(...

A variety $ X $ is $ F $-split if there exists an $ \mathcal{O}_{X} $-linear map $ \phi: F_{\ast}(\mathcal{O}_{X}) \to \mathcal{O}_{X} $ such that $ \phi \circ F^{\sharp} = \operatorname{id}_{\mathcal{O}_{X}} $. Such a map $ \phi $ is called a splitting. A closed sub-scheme $ Y $ of $ X $ is co...

This question was asked and correctly answered three weeks ago. Since then another user has posted, as of today, five other "answers" describing his thoughts about related questions, attempts that failed, etc. A week ago I suggested in a comment to him that these multiple answers are probably not...

This question was asked and correctly answered three weeks ago. Since then another user has posted, as of today, five other "answers" describing his thoughts about related questions, attempts that failed, etc. A week ago I suggested in a comment to him that these multiple answers are probably not...