Résumé : We study automorphism groups of complex K3 surfaces in the view of hyperbolicity. In particular, we show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic under the (optimal) assumption that the Picard number is greater than or equal to 6. This is a joint work in progress with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjing University).

Mots-Clés : K3 surfaces; hyperbolic group; genus one fibrations; Mordell-Weil groups