TY - BOOK ID - 65497300 TI - Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves PY - 2020 SN - 3030443299 3030443280 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Algebraic geometry. KW - Number theory. KW - Algebraic Geometry. KW - Number Theory. KW - Number study KW - Numbers, Theory of KW - Algebra KW - Algebraic geometry KW - Geometry KW - Vector bundles. KW - Fiber spaces (Mathematics) UR - https://www.unicat.be/uniCat?func=search&query=sysid:65497300 AB - 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. . ER -