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arXiv · 1912.09162

Non-archimedean integrals as limits of complex integrals

A. Ducros·E. Hrushovski·F. Loeser
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Abstract

We explain how non-archimedean integrals considered by Chambert-Loir and Ducros naturally arise in asymptotics of families of complex integrals. To perform this analysis we work over a non-standard model of the field of complex numbers, which is endowed at the same time with an archimedean and a non-archimedean norm. Our main result states the existence of a natural morphism between bicomplexes of archimedean and non-archimedean forms which is compatible with integration.

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A. Ducros, E. Hrushovski, F. Loeser. 2019-12-19. Non-archimedean integrals as limits of complex integrals. https://doi.org/10.1215/00127094-2022-0052

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