Arithmetic Geometry of Logarithmic Pairs a...

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Beschreibung

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes:

The basic notions of o-minimal geometry, which build to the proof of the Ax¿Schanuel conjecture for variations of Hodge structures;
A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective;
A systematic presentation and comparison between different notions of hyperbolicity,as an introduction to the Lang¿Vojta conjectures in the projective case;
An exploration of hyperbolicity and the Lang¿Vojta conjectures in the general case of quasi-projective varieties.

Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.

Über den Autor

Marc-Hubert Nicole is a professor of mathematics in the French university system.

Zusammenfassung

Introduces a number of exciting developments and cutting-edge results related to hyperbolicity, and the fundamental conjectures of Ax-Schanuel, Bombieri, Campana, Lang, Vojta, and others

Features chapters written by leading experts in their areas, collecting many of their own recent advances

Motivates a range of readers by presenting each chapter's respective material in a self-contained and accessible manner

Inhaltsverzeichnis

Lectures on the Ax-Schanuel Conjecture.- Arithmetic Aspects of Orbifold Pairs.- The Lang-Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties.- Hyperbolicity of Varieties of Log General Type.

Details

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 247 S. 19 s/w Illustr. 7 farbige Illustr. 247 p. 26 illus. 7 illus. in color.
ISBN-13:	9783030498665
ISBN-10:	3030498662
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Redaktion:	Nicole, Marc-Hubert
Herausgeber:	Marc-Hubert Nicole
Auflage:	1st edition 2020
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 15 mm
Von/Mit:	Marc-Hubert Nicole
Erscheinungsdatum:	01.11.2021
Gewicht:	0,4 kg

Artikel-ID: 120678941