Non-Archimedean integrals as limits of complex integrals
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 nonstandard model of the field of complex numbers, which is endowed at the same time with an Archimedean and a non...
Main Authors: | , , |
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Format: | Journal article |
Language: | English |
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Duke University Press
2023
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_version_ | 1797109348668801024 |
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author | Ducros, A Hrushovski, E Loeser, F |
author_facet | Ducros, A Hrushovski, E Loeser, F |
author_sort | Ducros, A |
collection | OXFORD |
description | 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 nonstandard 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. |
first_indexed | 2024-03-07T07:40:39Z |
format | Journal article |
id | oxford-uuid:3f5e20b5-f2bd-4970-b0b2-dfb707687178 |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-07T07:40:39Z |
publishDate | 2023 |
publisher | Duke University Press |
record_format | dspace |
spelling | oxford-uuid:3f5e20b5-f2bd-4970-b0b2-dfb7076871782023-04-27T08:34:45ZNon-Archimedean integrals as limits of complex integralsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3f5e20b5-f2bd-4970-b0b2-dfb707687178EnglishSymplectic ElementsDuke University Press2023Ducros, AHrushovski, ELoeser, FWe 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 nonstandard 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. |
spellingShingle | Ducros, A Hrushovski, E Loeser, F Non-Archimedean integrals as limits of complex integrals |
title | Non-Archimedean integrals as limits of complex integrals |
title_full | Non-Archimedean integrals as limits of complex integrals |
title_fullStr | Non-Archimedean integrals as limits of complex integrals |
title_full_unstemmed | Non-Archimedean integrals as limits of complex integrals |
title_short | Non-Archimedean integrals as limits of complex integrals |
title_sort | non archimedean integrals as limits of complex integrals |
work_keys_str_mv | AT ducrosa nonarchimedeanintegralsaslimitsofcomplexintegrals AT hrushovskie nonarchimedeanintegralsaslimitsofcomplexintegrals AT loeserf nonarchimedeanintegralsaslimitsofcomplexintegrals |