Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces

Released on by Marc-Hubert Nicole
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  • Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces Book Detail

  • Author : Marc-Hubert Nicole
  • Release Date : 2020-10-31
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 247
  • ISBN 13 : 3030498646
  • File Size : 22,22 MB
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Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces by Marc-Hubert Nicole PDF Summary

Book Description: 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.

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Lecture Notes on Diophantine Analysis

Lecture Notes on Diophantine Analysis

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These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathem