Overview
- Contains a complete account of the theta invariants
- Presents the author's theory of infinite Hermitian vector bundles over arithmetic curves
- Provides many interesting original insights and ties to other theories
Part of the book series: Progress in Mathematics (PM, volume 334)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions.
The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.
Reviews
“The monograph presents its interesting subject in a highly insightful, lucid, and accessible fashion; it will therefore be relevant to anyone with an interest in Arakelov geometry. While its results are technical, they are motivated, described and proved as clearly as can be.” (Jeroen Sijsling, zbMATH 1471.11002, 2021)
Authors and Affiliations
Bibliographic Information
Book Title: Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves
Authors: Jean-Benoît Bost
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-030-44329-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-44328-3Published: 22 August 2020
Softcover ISBN: 978-3-030-44331-3Published: 22 August 2021
eBook ISBN: 978-3-030-44329-0Published: 21 August 2020
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XXXIX, 365
Number of Illustrations: 1 b/w illustrations
Topics: Algebraic Geometry, Number Theory