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Introduction -- Metrized vector bundles: local theory -- Local metrics -- Adelic curves -- Vector bundles on adelic curves: global theory -- Slopes of tensor product -- Adelic line bundles on arithmetic varieties -- Nakai-Moishezon's criterion -- Reminders on measure theory.;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 Hermiti

Who reads Arakelov Geometry over Adelic Curves (Lecture Notes in Mathematics)?

Author

Chen, Huayi; Moriwaki, Atsushi

Publisher

Springer Singapore, Imprint Springer

Published

2020

Language

EN

ISBN

9781881881919

Category

nonfiction

Subjects

Mathematics, Stem