LEADER 03985nam 22005415 450 001 9910483839003321 005 20250610110151.0 010 $a3-030-44329-9 024 7 $a10.1007/978-3-030-44329-0 035 $a(CKB)4100000011392591 035 $a(DE-He213)978-3-030-44329-0 035 $a(MiAaPQ)EBC6317292 035 $a(PPN)250215020 035 $a(MiAaPQ)EBC6317256 035 $a(MiAaPQ)EBC29090898 035 $a(EXLCZ)994100000011392591 100 $a20200821d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTheta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves /$fby Jean-Benoît Bost 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (XXXIX, 365 p. 1 illus.) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v334 311 08$a3-030-44328-0 327 $aIntroduction -- 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. 330 $aThis book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication. . 410 0$aProgress in Mathematics,$x0743-1643 ;$v334 606 $aGeometry, Algebraic 606 $aNumber theory 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aGeometry, Algebraic. 615 0$aNumber theory. 615 14$aAlgebraic Geometry. 615 24$aNumber Theory. 676 $a514.224 700 $aBost$b Jean-Benoît$4aut$4http://id.loc.gov/vocabulary/relators/aut$062634 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483839003321 996 $aTheta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves$92391164 997 $aUNINA