模糊复指数化
Blurred Complex Exponentiation
摘要：
它表明，复杂的领域配备了“近似指数映射”，定义为从一个小组的模糊性，是quasiminimal：每个自同构不变的字段的子集是可数或共可数。如果模糊性被认为是从一个类似于常数场的子域，则所得到的“模糊指数场”同构于齐伯指数场的等效模糊的结果，以及差分闭合场的适当约简。这些结果是对Zilber关于复指数场本身是拟极小的猜想的进一步发展。证明中的一个关键因素是证明模拟的指数代数封闭性属性使用的密度组管理的模糊性相对于复杂的拓扑结构。
英文摘要：
It is shown that the complex field equipped with the "approximate exponential map", defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset of the field is countable or co-countable. If the ambiguity is taken to be from a subfield analogous to a field of constants then the resulting "blurred exponential field" is isomorphic to the result of an equivalent blurring of Zilber's exponential field, and to a suitable reduct of a differentially closed field. These results are progress towards Zilber's conjecture that the complex exponential field itself is quasiminimal. A key ingredient in the proofs is to prove the analogue of the exponential-algebraic closedness property using the density of the group governing the ambiguity with respect to the complex topology.
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