| 期刊全称 | Arakelov Geometry over Adelic Curves | | 影响因子2023 | Huayi Chen,Atsushi Moriwaki | | 视频video | | | 发行地址 | Introduces a new mathematical theory having strong links with several research domains.Opens new research topics with original research results; attracts attention from researchers and graduate studen | | 学科分类 | Lecture Notes in Mathematics | | 图书封面 |  | | 影响因子 | The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on ananalogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational | | Pindex | Book 2020 |
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发表于 2025-3-21 18:44:27
