Arithmetic algebraic geometry, roughly speaking, the study of schemes of finite type over the spectrum of Z, was developed along with the invention of scheme theory by Grothendieck and others in 1960’s. In the past half century, it has been the most influential area of number theory research. Great mathematicians such as Serre, Tate, Deligne, Faltings and Wiles played important roles in the development of arithmetic geometry. As a consequence, great theorems such as Fermat’s Last Theorem, Weil Conjecture and Mordell Conjecture were proved. It is one of the main fronts for current mathematical research.

In 2003, Professor Jean-Marc Fontaine was hired as Chair Professor at Tsinghua University. Since then, in slightly more than 3 years Fontaine and his team (Illusie, Raynaud, Colmez, Ullmo, Colliot-Thélène, Gille, Harari, and Fargues) gave courses and trained students at Tsinghua. Many talented Chinese students were selected to continue their graduate study at France. In August 2005 an international summer school and a Sino-French conference on arithmetic geometry and automorphic forms were held at Tsinghua and Chern Institute of Mathematics at Nankai respectively. These activities opened the door of cooperation in number theory between China and France. The aim of this second Sino-French conference (compare to the first one in 2005) is to celebrate the successful cooperation between China and France, to enhance this cooperation, and to showcase the state of the art in number theory.