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.
Jean-Benoît Bost
Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves [PDF ebook]
Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves [PDF ebook]
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Langue Anglais ● Format PDF ● Pages 365 ● ISBN 9783030443290 ● Taille du fichier 3.5 MB ● Maison d’édition Springer International Publishing ● Lieu Cham ● Pays CH ● Publié 2020 ● Téléchargeable 24 mois ● Devise EUR ● ID 7579934 ● Protection contre la copie DRM sociale