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...
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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 |