Explore: Néron Models

this scheme is the Néron model of A. In general the scheme AK need not have any Néron model. For abelian varieties AK Néron models exist and are unique

A-algebra. Bosch, Siegfried; Lütkebohmert, Werner; Raynaud, Michel (1990). Néron models. Berlin: Springer-Verlag. p. 191. The original reference is Section 1

together with tools from algebraic geometry, including the theory of Néron models. The main idea of Faltings's proof is the comparison of Faltings heights

André Néron, a mathematician, who introduced: Néron minimal model Néron differential Néron–Severi group Néron–Ogg–Shafarevich criterion Néron–Tate height

{\displaystyle A} . The Néron model is a smooth group scheme, so we can consider A 0 {\displaystyle A^{0}} , the connected component of the Néron model which contains

defined over a local field or global field. The Néron differential behaves well on the Néron minimal models. For an elliptic curve of the form y 2 + a 1

reference Siegfried Bosch; Werner Lütkebohmert; Michel Raynaud (1990). Néron Models. Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge. Vol. 21

discovered the Néron minimal model of an elliptic curve or abelian variety, the Néron differential, the Néron–Severi group, the Néron–Ogg–Shafarevich

Tate (1975) as an improvement of the description of the Néron model of an elliptic curve by Néron (1964). Assume that all the coefficients of the equation

refined theory of (in effect) a right adjoint to reduction mod p — the Néron model — cannot always be avoided. In the case of an elliptic curve there is