Some model theory of compact complex spaces
Some model theory of compact complex spaces
复制标题
紧复空间的一些模型理论
DOI：
10.1090/conm/270/04380
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发表时间：
2000
影响因子：
1.3
通讯作者：
A. Pillay
中科院分区：
文献类型：
--
作者：
A. Pillay
我们对紧致复流形的范畴C作了一些观察，认为它是有限Morley秩的多分类结构。我们还指出，Mordell-lang猜想对复环面成立：如果A是复环面，Γ是A的有限生成子群，X是A的解析子簇，则X∩Γ是A的子群的平移的有限并。这在文献中是隐含的，但我们给出了交换簇的初等约化。我们讨论了C与有限维微分代数集范畴之间的类比。(还包括对Mordell-Lang猜想和模型理论贡献的简要概述。)
We make several observations about the category C of compact complex manifolds, considered as a many-sorted structure of finite Morley rank. We also point out that the Mordell-Lang conjecture holds for complex tori: if A is a complex torus, Γ a finitely generated subgroup of A, and X an analytic subvariety of A, then X ∩ Γ is a finite union of translates of subgroups of A. This is implicit in the literature but we give an elementary reduction to the abelian variety case. We discuss analogies between C and the category of finite dimensional differential algebraic sets. (A brief survey of the Mordell-Lang conjecture and model-theoretic contributions is also included.)