Endomorphisms of symbolic algebraic varieties
Endomorphisms of symbolic algebraic varieties
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DOI：
10.1007/pl00011162
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发表时间：
1999-06
影响因子：
2.6
通讯作者：
M. Gromov
中科院分区：
文献类型：
--
作者：
M. Gromov
Ax定理指出，复代数簇的任何正则自映射要么是满射的，要么是非内射的；这一性质被称为连通性，本文在前代数空间的正则映射范畴中研究了这一性质。我们证明了这样的映射是附加性的，如果它们与足够大的自同构群交换。特别令人感兴趣的是无穷图上的前代数变差。本文旨在揭示模型论、代数几何和符号动力学之间的关系。
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory, algebraic geometry, and symbolic dynamics.