國立虎尾科技大學 |

Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves/ by Jean-Benoît Bost.
Author:	Bost, Jean-Benoît.
Description:	XXXIX, 365 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebraic geometry. -
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-Benoît.

Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves[electronic resource] /by Jean-Benoît Bost. - 1st ed. 2020. - XXXIX, 365 p. 1 illus.online resource. - Progress in Mathematics,3340743-1643 ;. - Progress in Mathematics,312.

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 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.

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:

1255324
Algebraic geometry.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves
LDR:03516nam a22004095i 4500 001 1024916
003 DE-He213
005 20200821183859.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030443290 $9 978-3-030-44329-0
024 7 $a 10.1007/978-3-030-44329-0 $2 doi
035 $a 978-3-030-44329-0
050 4 $a QA564-609
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
100 1 $a Bost, Jean-Benoît. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321122
245 1 0 $a Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves $h [electronic resource] / $c by Jean-Benoît Bost.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XXXIX, 365 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Progress in Mathematics, $x 0743-1643 ; $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 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.
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 Algebraic geometry. $3 1255324
650 0 $a Number theory. $3 527883
650 1 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Number Theory. $3 672023
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030443283
776 0 8 $i Printed edition: $z 9783030443306
776 0 8 $i Printed edition: $z 9783030443313
830 0 $a Progress in Mathematics, $x 0743-1643 ; $v 312 $3 1258196
856 4 0 $u https://doi.org/10.1007/978-3-030-44329-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)