平坦性的下降与直和项猜想
Descent of Flatness and the Direct Summand Conjecture
摘要：
本文的中心定理证明了：若$R$是完备正则局部环，且$B$是$R$在$R$的分式域的代数闭包中的整闭包，则$\Hom_R(B, R) \neq 0$ .我们对这个定理的证明几乎不涉及数学，它适用于所有特征。作为推论，我们得到了a）诺特环的整扩张的平坦性下降和b）由M.霍克斯特
英文摘要：
In the central theorem of this article we prove the following: if $R$ is a complete regular local ring and $B$ is the integral closure of $R$ in the algebraic closure of the fraction field of $R$, then $\Hom_R(B, R) \neq 0$. Our proof of this theorem does not involve almost mathematics and it works for all characteristics. As consequences we derive the validity of a) descent of flatness for integral extensions of Noetherian rings and b) direct summand conjecture due to M. Hochster.
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