In mathematics, the NĂ©ronâOggâShafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and â is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if the â-adic Tate module Tâ of A is unramified. Andrew Ogg ( 1967) introduced the criterion for elliptic curves. Serre and Tate ( 1968) used the results of AndrĂ© NĂ©ron ( 1964) to extend it to abelian varieties, and named the criterion after Ogg, NĂ©ron and Igor Shafarevich (commenting that Ogg's result seems to have been known to Shafarevich).
In mathematics, the NĂ©ronâOggâShafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and â is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if the â-adic Tate module Tâ of A is unramified. Andrew Ogg ( 1967) introduced the criterion for elliptic curves. Serre and Tate ( 1968) used the results of AndrĂ© NĂ©ron ( 1964) to extend it to abelian varieties, and named the criterion after Ogg, NĂ©ron and Igor Shafarevich (commenting that Ogg's result seems to have been known to Shafarevich).