Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves
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Beschreibung
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.
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.
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
Autor*in
Jean-Benoît Bost
Themen in »Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves«
geometry of numbers (Euclidean lattices) transcendence theory arithmetic curve Diophantine geometry Arakelov geometry
Stimmen zu »Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves«
“The Preface and the Introduction give an extremely well-done overview of the contents of the book, meant for a wide scope of readers. … What results is a carefully written very readable text.” (Rolf Berndt, Mathematical Reviews, April, 2022)
“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)
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