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.
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