混合特征双根扩张上双有理极大Cohen-Macaulay模的存在性
On the existence of birational maximal Cohen-Macaulay modules over biradical extensions in mixed characteristic
摘要：
设$S$是混合特征$p\geq 3$的非分歧正则局部环，$S^p$是$S$的子环，它是将$S/pS$上的Frobenius映射的像提升到$S$而得到的.设$R$是$S$在其商域的次$p^2$的双根扩张中的整闭包，该扩张是通过邻接充分一般的平方自由元$f,g\in S^p$的$p$次根得到的.证明了$R$允许一个双有理极大Cohen-Macaulay模.注意，$R$不自动为Cohen-Macaulay。
英文摘要：
Let $S$ be an unramified regular local ring of mixed characteristic $p\geq 3$ and $S^p$ the subring of $S$ obtained by lifting to $S$ the image of the Frobenius map on $S/pS$. Let $R$ be the integral closure of $S$ in a biradical extension of degree $p^2$ of its quotient field obtained by adjoining $p$-th roots of sufficiently general square free elements $f,g\in S^p$. We show that $R$ admits a birational maximal Cohen-Macaulay module. It is noted that $R$ is not automatically Cohen-Macaulay.
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