Construction de courbes sur les surfaces K3 [d'apr\`es Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]

TL;DR

This paper discusses recent advances in constructing curves on K3 surfaces, including proofs of the Tate conjecture in odd characteristic and the existence of infinitely many rational curves on many K3 surfaces.

Contribution

It presents new proofs of the Tate conjecture for K3 surfaces in odd characteristic and demonstrates the construction of infinitely many rational curves on various K3 surfaces.

Findings

Proof of Tate conjecture for K3 surfaces in odd characteristic

Construction of infinitely many rational curves on K3 surfaces

Advances based on work by Maulik, Charles, Madapusi Pera, Bogomolov-Hassett-Tschinkel, Li-Liedtke

Abstract

We report on recent results concerning the construction of curves on K3 surfaces: the proof of the Tate conjecture for K3 surfaces in odd characteristic (after Maulik, Charles and Madapusi Pera), and the construction of infinitely many rational curves on many K3 surfaces (after Bogomolov-Hassett-Tschinkel and Li-Liedtke).