Introductory material
We will assume basic algebraic number theory, some exposure to
algebraic geometry, and knowledge of sections 1-3 of Marker's notes on
model theory.
Shimura varieties.
Pierre Deligne, Travaux de Griffiths, Séminaire BOURBAKI
22e année, 1969/70, no 376, mai-juin 1970.
Pierre Deligne, Travaux
de Shimura, Séminaire BOURBAKI
23e année, 1970/71, no 389, février 1971.
J. S. Milne, Introduction
to Shimura varieties, Clay Mathematical Proceedings Volume 4,
2005, 265-378.
Algebraic geometry
Marc
Hindry,
Introduction to Abelian Varieties
and the Mordell-Lang Conjecture.
E. Bombieri, W. Gubler, Heights in diophantine Geometry, Cambridge
University Press 2006.
M. Hindry, J. Silverman, Diophantine Geometry: an introduction, Springer
2000.
Model Theory.
In addition to sections 1-3 of Dave Marker's course
notes, we suggest that people read sections 4-7 and the
Appendix.
Course Model Theory for Algebra and Algebraic Geometry, by Dave
Marker. Orsay, Spring 2010. Content:
Sections 1--3: Language, Structures and Theories, The Compactness Theorem,
Ultraproducts and Compactness
Sections 4-6: Complete Theories, Quantifier Elimination, Algebraically Closed Fields
Section 7: Real Closed Fields and o-minimality
Section 8: The Pila-Zannier proof of the Manin-Mumford
Conjecture
Appendix: Real Algebra
Exercises using the Compactness Theorem
More advanced material
Thomas Scanlon, A proof of the André-Oort conjecture via
mathematical logic [after Pila, Wilkie, Zannier]. April 2011, Bourbaki
seminar.
Antoine Chambert-Loir, Relations de dépendance et
intersections exceptionnelles, Séminaire Bourbaki, 63e
année, 2010-2011, exposé No
1032. arXiv:1011.4738
L. van den Dries, Tame topology and o-minimal structures, Cambridge Univ. Press, New York, 1998
U. Zannier, Some Problems of Unlikely Intersections in Arithmetic and
Geometry, with Appendices by D. Masser (Annals of Mathematics Studies,
Am-181), Princeton UP, 2012
Handouts
of the workshop The Zilber-Pink conjecture, Luminy, 16-20 May
2011. Content:
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