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Theta invariants of Euclidean lattic...

Bost, Jean-Benoit.

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Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves/ by Jean-Benoit Bost.
Author:	Bost, Jean-Benoit.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xxxix, 365 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Hermitian vector bundles over arithmetic curves -- θ-Invariants of Hermitian vector bundles over arithmetic curves -- Geometry of numbers and θ-invariants -- Countably generated projective modules and linearly compact Tate spaces over Dedekind rings -- Ind- and pro-Hermitian vector bundles over arithmetic curves -- θ-Invariants of infinite dimensional Hermitian vector bundles: denitions and first properties -- Summable projective systems of Hermitian vector bundles and niteness of θ-invariants -- Exact sequences of infinite dimensional Hermitian vector bundles and subadditivity of their θ-invariants -- Infinite dimensional vector bundles over smooth projective curves -- Epilogue: formal-analytic arithmetic surfaces and algebraization -- Appendix A. Large deviations and Cramer'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.
Contained By:	Springer Nature eBook
Subject:	Vector bundles. -
Online resource:	https://doi.org/10.1007/978-3-030-44329-0
ISBN:	9783030443290

Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves
Bost, Jean-Benoit.

Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves[electronic resource] /by Jean-Benoit Bost. - Cham :Springer International Publishing :2020. - xxxix, 365 p. :ill., digital ;24 cm. - Progress in mathematics,v.3340743-1643 ;. - Progress in mathematics ;v.334..

Introduction -- Hermitian vector bundles over arithmetic curves -- θ-Invariants of Hermitian vector bundles over arithmetic curves -- Geometry of numbers and θ-invariants -- Countably generated projective modules and linearly compact Tate spaces over Dedekind rings -- Ind- and pro-Hermitian vector bundles over arithmetic curves -- θ-Invariants of infinite dimensional Hermitian vector bundles: denitions and first properties -- Summable projective systems of Hermitian vector bundles and niteness of θ-invariants -- Exact sequences of infinite dimensional Hermitian vector bundles and subadditivity of their θ-invariants -- Infinite dimensional vector bundles over smooth projective curves -- Epilogue: formal-analytic arithmetic surfaces and algebraization -- Appendix A. Large deviations and Cramer'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.

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.

ISBN: 9783030443290

Standard No.: 10.1007/978-3-030-44329-0doiSubjects--Topical Terms:

597540
Vector bundles.

LC Class. No.: QA612.63

Dewey Class. No.: 514.224

Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves
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100 1 $a Bost, Jean-Benoit. $3 3236674
245 1 0 $a Theta invariants of Euclidean lattices and infinite-dimensional Hermitian vector bundles over arithmetic curves $h [electronic resource] / $c by Jean-Benoit Bost.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a xxxix, 365 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.334
505 0 $a Introduction -- Hermitian vector bundles over arithmetic curves -- θ-Invariants of Hermitian vector bundles over arithmetic curves -- Geometry of numbers and θ-invariants -- Countably generated projective modules and linearly compact Tate spaces over Dedekind rings -- Ind- and pro-Hermitian vector bundles over arithmetic curves -- θ-Invariants of infinite dimensional Hermitian vector bundles: denitions and first properties -- Summable projective systems of Hermitian vector bundles and niteness of θ-invariants -- Exact sequences of infinite dimensional Hermitian vector bundles and subadditivity of their θ-invariants -- Infinite dimensional vector bundles over smooth projective curves -- Epilogue: formal-analytic arithmetic surfaces and algebraization -- Appendix A. Large deviations and Cramer'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.
520 $a 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.
650 0 $a Vector bundles. $3 597540
650 0 $a Arithmetical algebraic geometry. $3 699672
650 0 $a Lattice theory. $3 532024
650 0 $a Hermitian symmetric spaces. $3 711293
650 1 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Number Theory. $3 891078
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773 0 $t Springer Nature eBook
830 0 $a Progress in mathematics ; $v v.334. $3 3526042
856 4 0 $u https://doi.org/10.1007/978-3-030-44329-0
950 $a Mathematics and Statistics (SpringerNature-11649)