香蕉视频

Title:聽An introduction to the Shafarevich's conjecture.

Abstract:聽In his 1962 ICM talk I. R. Shafarevich made several significant conjectures about the geometry and arithmetic of the moduli space of genus g curves. A. Parshin and A. Arakelov verified the function field version of Shafarevich's conjecture, while the number field version was proved by Faltings in his famous 1983 paper, as an intermediate step in his proof of the Mordell conjecture. In this talk, we will give an introduction to the moduli space of genus g curves and the geometric aspect of the Shafarevich's conjecture. The main steps in Parshin and Arakelov's proof will be explained. I will also sketch what is known today about the moduli spaces of higher dimensional projective manifolds.

Venue

CRM, 4336-4384 Pavillon Aisenstadt, UdeM