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Preprint Number 1813

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1813. Johan Commelin, Annette Huber
Exponential periods and o-minimality II
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Submission date: 16 July 2020

Abstract:

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 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.

Mathematics Subject Classification: 11G35, 14F25, 14F40, 14P10, 03C64

Keywords and phrases:

Full text arXiv 2007.08290: pdf, ps.


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