ACFA和T_A中的群样极小集
Grouplike minimal sets in ACFA and in T_A
摘要：
本文是作者关于ACFA的博士论文的一部分的推广，最后给出了T_A中可定义群的一个刻画。本文研究了ACFA中“p位于代数曲线A上且s（x）=f（x）”形式的极小公式，其中s是A到s（A）的支配有理函数f，其中s是自同构.这些被证明是均匀的，在Zilber的分割，和对（A，f），落入每一个的三种情况下的特点。这些特征在家族中是可定义的。本文涵盖了大约一半的论文，即那些部分，它可以纯粹的模型理论从ACFA，模型伴侣类的代数闭域的自同态，到T_A，模型伴侣类的模型的任意全超越理论T的内射自同态，如果这个模型伴侣存在。在这个过程中，得到了ACFA中可定义群的特征的T_A模拟。充分表征是从这些中间结果与大量使用代数几何：见论文或即将发表的论文“围绕拉茨函数”。
英文摘要：
This paper began as a generalization of a part of the author's PhD thesis about ACFA and ended up with a characterization of groups definable in T_A. The thesis concerns minimal formulae in ACFA of the form "p lies on an algebraic curve A and s(x)=f(x)" for some dominant rational function f from A to s(A), where s is the automorphism. These are shown to be uniform in the Zilber trichotomy, and the pairs (A,f) that fall into each of the three cases are characterized. These characterizations are definable in families. This paper covers approximately half of the thesis, namely those parts of it which can be made purely model-theoretic by moving from ACFA, the model companion of the class of algebraically closed fields with an endomorphism, to T_A, the model companion of the class of models of an arbitrary totally-transcendental theory T with an injective endomorphism, if this model-companion exists. A T_A analog of the characterization of groups definable in ACFA is obtained in the process. The full characterization is obtained from these intermediate results with heavy use of algebraic geometry: see the thesis or the forthcoming paper "Around Lattes functions".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
