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.
