Affine curves in characteristicp are set theoretic complete intersections
Affine curves in characteristicp are set theoretic complete intersections
复制标题
特征p中的仿射曲线是设定的理论完全交点
DOI：
10.1007/bf01390268
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发表时间：
1978
影响因子：
3.1
通讯作者：
M. Nori
中科院分区：
文献类型：
--
作者：
R. Cowsik;M. Nori
本文证明了正特征p的域k上仿射n-空间中的任何曲线都是集合论完全交。Szpiro证明了在仿射3-空间中局部完全交的曲线是集合论完全交。参见Ferrand [1]，Szpiro [-2]。Mohan Kumar的文章[3]的一个推论是：任何仿射n空间中的任何局部完全交曲线都是集合论完全交。在这里，我们首先证明结果在完全的局部情况下，并使用它来证明一般结果。[We应只考虑具有积极特征的领域。定理1.令R= k [[X 1，X 2.] Xn]]是k上的形式幂级数环，k是正特征p的理想域.设I是R中的根理想，使得dim（R/I）= 1.然后存在理想J=（Ya，Y2. Y，-1），使得基团J= I。
We prove here that any curve in the affine n-space over a field k of positive characteristic p is a set theoretic complete intersection. Szpiro proved that a curve which is a local complete intersection in affine 3-space is a set theoretic complete intersection. See, Ferrand [1], Szpiro [-2]. A consequence of Mohan Kumar's paper [3] is that any local complete intersection curve in any affine nspace is a set theoretic complete intersection. We here first prove the result in the complete local case and use that to prove the general result.[We shall only consider fields of positive characteristic.]Theorem 1. Let R= k [[X 1, X 2..... Xn]] be the ring of formal power series over k, a perfect field of positive characteristic p. Let I be a radical ideal in R such that dim (R/I)= 1. Then there is an ideal J=(Ya, Y2..... Y,-1) in R such that radical J= I.