Time：9:50-12:15, June 15/22, 13:30-15:55, June 18, 2026
Venue：E13-128
Course: Arithmetic vanishing in Arakelov geometry
Speaker：Christophe Soulé
Abstract:
Lecture 1: Minkowski's and Riemann-Roch theorems.
With Gillet, we prove a result for euclidean lattices and their duals which completes the analogy between the Minkowski's theorem and the Riemann-Roch theorem for curves.
Lecture 2: An inequality of Miyaoka and Moriwaki.
Let E be a rank two vector bundle on an arithmetic surface, and let h be an Einstein-Hermitian metric on the complex vector bundle defined by E. We prove the inequality c_1(E,h)^2 <= 4 c_2(E,h).
Lecture 3: An arithmetic vanishing theorem.
We prove an arithmetic analog of the Kodaira's vanishing theorem: if L is a positive line bundle on some arithmetic surface and if h is a positive metric on L, there exists no extension class in H^1(X,L^{-1}) of small norm.
