The Supersingular Locus of Hilbert Modular Surfaces modulo p by

1Acknowledgments: The two main mathematical projects I tried working on with the best of my energies in the last year and a half have been the book “Lecture Notes on Hilbert Modular Varieties and Modular Forms”, assisting Prof. Eyal Z. Goren, and this thesis. Accepting to study and work with Prof. Goren has clearly been the single most labor-inducing decision in my mathematical life. In spite of his occasional despotic surges, I thank him for the great opportunity, for its incredible availability, for his precise and intelligent answers to my often vague, ill-formulated questions, for abundantly sharing his insights and for his extensive editing of this thesis. On the mathematical level, I would also like to thank my fellow students in num-ber theory, especially Ignazio Longhi for many exchanges and dicussions, including a well-articulated introduction to rigid analytic geometry; and Lassina Dembele, for his enthusiasm and competence at discussing algebraic geometry. I would also like to thank the organizers and participants of the 1998-1999 Theme Year in Number Theory and Arithmetic Geometry at the Centre de recherches mathé-matiques for such a challenging and thought-provoking year