Arakelov Geometry and Diophantine Applications

Häftad, Engelska, 2021

Del 2276 i serien Lecture Notes in Mathematics

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Beskrivning

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied.

Produktinformation

Utgivningsdatum:2021-03-11
Mått:155 x 235 x 29 mm
Vikt:730 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:469
Förlag:Springer Nature Switzerland AG
ISBN:9783030575588

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Innehållsförteckning

- Introduction. - Part A Concepts of Arakelov Geometry. - Chapter I: Arithmetic Intersection. - Chapter II: Minima and Slopes of Rigid Adelic Spaces. - Chapter III : Introduction aux théorèmes de Hilbert-Samuel arithmétiques. - Chapter IV: Euclidean Lattices, Theta Invariants, and Thermodynamic Formalism. - Part B Distribution of Rational Points and Dynamics. - Chapter V: Beyond Heights: Slopes and Distribution of Rational Points. - Chapter VI: On the Determinant Method and Geometric Invariant Theory. - Chapter VII: Arakelov Geometry, Heights, Equidistribution, and the Bogomolov Conjecture. - Chapter VIII : Autour du théorème de Fekete-Szeg˝o. - Chapter IX: Some Problems of Arithmetic Origin in Rational Dynamics. - Part C Shimura Varieties. - Chapter XI: The Arithmetic Riemann–Roch Theorem and the Jacquet–Langlands Correspondence. - Chapter XII: The Height of CM Points on Orthogonal Shimura Varieties and Colmez’s Conjecture.