指数周期与o-极小性II
Exponential periods and o-minimality II
摘要：
本文是作者与Philipp Habegger共同撰写的“指数周期和o-极小性I”的续篇。我们完成了指数周期的不同定义之间的比较，并表明它们都导致相同的概念。在第一篇文章中，我们证明了朴素指数周期是绝对收敛的指数周期。我们还表明，天真的指数期的符号体积的可定义集的O-最小结构产生的$\mathbb{Q}$，真正的指数函数和${\sin}|_{[0,1]}$。在本文中，我们比较这些定义与上同调指数周期和指数Nori动机的周期。特别地，朴素指数周期与指数Nori动机的周期相同，这证明朴素指数周期的定义挑选出了正确的复数集合称为指数周期。
英文摘要：
This paper is a sequel to "Exponential periods and o-minimality I" that the authors wrote together with Philipp Habegger. We complete the comparison between different definitions of exponential periods, and show that they all lead to the same notion. In the first paper, we show that naive exponential periods are absolutely convergent exponential periods. We also show that naive exponential periods are up to signs volumes of definable sets in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,1]}$. In this paper, we compare these definitions with cohomological exponential periods and periods of exponential Nori motives. In particular, naive exponential periods are the same as periods of exponential Nori motives, which justifies that the definition of naive exponential periods singles out the correct set of complex numbers to be called exponential periods.
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