The divisor class groups of some rings of holomorphic functions
The divisor class groups of some rings of holomorphic functions
复制标题
全纯函数某些环的约数类群
DOI：
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发表时间：
1971
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通讯作者：
David Prill
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文献类型：
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作者：
David Prill
设(X，XO)是正规复解析空间，⋐X是连通的Stein紧集，即X的一个紧子集，它的基是开邻域，它是Stein空间。我们把注意力限制在那些A上，使得R=H0O)是诺德的。在第一节中，给出了涉及除数类群OFR的各种精确序列，记为C(R)。(IFA是一个点，其中一个序列是众所周知的[24]，[39]。)设B是正规簇Y上的连通紧Stein集，使得=Ho(B，Yo)和T=Ho(A×B，X×Yo)是Notherian的。在第二章中，我们给出了一个与C(R)、C(S)和DC(T)有关的Künneth型公式。在第三章中，我们证明了某些解析局部环是唯一因式分解整环，研究了有限群在解析空间的商上的局部环的除子类群，并证明了关于复解析集芽拓扑的一个简单结果。我们给出了一个函数论证明，具有孤立奇点的维大于3的完全交有局部环，局部环是唯一的因式分解整环。
Let (X,xO) be a normal complex analytic space andA⋐X a connected Stein compact set, i.e. a compact subset ofX which has a basis of open neighborhoods which are Stein spaces. We restrict attention to thoseA such thatR=H0O) is Noetherian. In Section I various exact sequences involving the divisor class group ofR, denotedC(R), are developed. (IfA is a point, one of these sequences is well-known [24], [39].)LetB be a connected compact Stein set on a normal varietyY such thatS=Ho(B,YO) andT=Ho(A×B,X×YO are Noetherian. In II we give a Künneth-type formula which relatesC(R), C(S) andC(T). In III we show certain analytic local rings are unique factorization domains, study the divisor class groups of local rings on the quotient of an analytic space by a finite group, and prove a simple result on the topology of germs of complex analytic sets. We give a function-theoretic proof that complete intersections of dimensions greater than three which have isolated singularities have local rings which are unique factorization domains.