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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves : Progress In Mathematics - Jean-Benoît Bost

Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

By: Jean-Benoît Bost

Hardcover | 22 August 2020

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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.


Industry Reviews
"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)

You Can Find This Book In

Non-FictionMathematicsGeometryAlgebraic GeometryNumber Theory

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