He discovered the Néron minimal model of an elliptic curve or abelian variety, the Néron differential, the Néron–Severi group, the Néron–Ogg–Shafarevich criterion, the local height and Néron–Tate height of rational points on an abelian variety over a discrete valuation ring or Dedekind domain, and classified the possible fibers of an elliptic fibration.
He introduced the Néron minimal model of an elliptic curve or abelian variety, the Néron differential, the Néron–Severi group, and the Néron–Ogg–Shafarevich criterion, which are fundamental concepts in number theory. He also classified the possible fibers of an elliptic fibration.