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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves 2020 ed. [Mīkstie vāki]

  • Formāts: Paperback / softback, 365 pages, height x width: 235x155 mm, weight: 623 g, 1 Illustrations, black and white; XXXIX, 365 p. 1 illus., 1 Paperback / softback
  • Sērija : Progress in Mathematics 334
  • Izdošanas datums: 22-Aug-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • ISBN-10: 3030443310
  • ISBN-13: 9783030443313
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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves 2020 ed.Palielināt
  • Formāts: Paperback / softback, 365 pages, height x width: 235x155 mm, weight: 623 g, 1 Illustrations, black and white; XXXIX, 365 p. 1 illus., 1 Paperback / softback
  • Sērija : Progress in Mathematics 334
  • Izdošanas datums: 22-Aug-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • ISBN-10: 3030443310
  • ISBN-13: 9783030443313
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783030443313.html
Keywords:

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. 


Recenzijas

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)

Introduction.- Hermitian vector bundles over arithmetic
curves.- -Invariants of Hermitian vector bundles over arithmetic
curves.- Geometry of numbers and -invariants.- Countably generated
projective modules and linearly compact Tate spaces over Dedekind
rings.- Ind- and pro-Hermitian vector bundles over arithmetic
curves.- -Invariants of infinite dimensional Hermitian vector bundles:
denitions and first properties.- Summable projective systems of Hermitian
vector bundles and niteness of -invariants.- Exact sequences of infinite
dimensional Hermitian vector bundles and subadditivity of
their -invariants.- Infinite dimensional vector bundles over smooth
projective curves.- Epilogue: formal-analytic arithmetic surfaces and
algebraization.- Appendix A. Large deviations and Cramér's theorem.- Appendix
B. Non-complete discrete valuation rings and continuity of linear forms
on prodiscrete modules.- Appendix C. Measures on countable sets and their
projective limits.- Appendix D. Exact categories.- Appendix E. Upper bounds
on the dimension of spaces of holomorphic sections of line bundles over
compact complex manifolds.- Appendix F. John ellipsoids and finite
dimensional normed spaces.