有限域上含子概型超曲面截面的Bertini定理
Bertini theorems for hypersurface sections containing a subscheme over finite fields
摘要：
在一定维数条件下，证明了包含有限域上射影空间的闭子概形且与光滑拟射影概形光滑相交的超曲面的存在性.这推广了一个贝尔蒂尼定理Poonen和有限域类似的贝尔蒂尼定理Altman和Kleiman。此外，我们增加了修改超曲面的许多局部条件的可能性。我们证明了对于具有简单正规交叉的格式，维数条件是满足的，并给出了嵌入到光滑概形中的应用。
英文摘要：
We show the existence of a hypersurface that contains a given closed subscheme of a projective space over a finite field and intersects a smooth quasi-projective scheme smoothly, under some condition on the dimension. This generalizes a Bertini theorem by Poonen and is the finite field analogue of a Bertini theorem by Altman and Kleiman. Furthermore, we add the possibility of modifying finitely many local conditions of the hypersurface. We show that the condition on the dimension is fulfilled for schemes with simple normal crossings and give an application to embeddings into smooth schemes.
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