In mathematics, the Néron–Ogg–Shafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and ℓ is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if the ℓ-adic Tate module Tℓ of A is unramified. Andrew Ogg introduced the criterion for elliptic curves. Serre and Tate used the results of André Néron to extend it to abelian varieties,and named the criterion after Ogg, Néron and Igor Shafarevich (commenting that Ogg's result seems to have been known to Shafarevich).
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| - Néron–Ogg–Shafarevich criterion (en)
- Néron–Ogg–Sjafarevitjs kriterium (sv)
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| - In mathematics, the Néron–Ogg–Shafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and ℓ is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if the ℓ-adic Tate module Tℓ of A is unramified. Andrew Ogg introduced the criterion for elliptic curves. Serre and Tate used the results of André Néron to extend it to abelian varieties,and named the criterion after Ogg, Néron and Igor Shafarevich (commenting that Ogg's result seems to have been known to Shafarevich). (en)
- Inom matematiken är Néron–Ogg–Sjafarevitjs kriterium ett resultat som säger att en elliptisk kurva eller abelsk varietet A över en K har god reduktion om och bara om det finn ett primtal ℓ som inte delar karakteristiken av av K (eller ekvivalent för alla sådana primtal) så att den ℓ-adiska Tℓ av A är . introducerade kriteriet för elliptiska kurvor. Serre och använde resultat av till att utvidga den till abelska varieteter, samt uppkallade resultatet efter Ogg, Néron och (de sade att Oggs resultat verkat vara känt för Sjafarevitj). (sv)
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| - André Néron (en)
- Andrew Ogg (en)
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| - In mathematics, the Néron–Ogg–Shafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and ℓ is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if the ℓ-adic Tate module Tℓ of A is unramified. Andrew Ogg introduced the criterion for elliptic curves. Serre and Tate used the results of André Néron to extend it to abelian varieties,and named the criterion after Ogg, Néron and Igor Shafarevich (commenting that Ogg's result seems to have been known to Shafarevich). (en)
- Inom matematiken är Néron–Ogg–Sjafarevitjs kriterium ett resultat som säger att en elliptisk kurva eller abelsk varietet A över en K har god reduktion om och bara om det finn ett primtal ℓ som inte delar karakteristiken av av K (eller ekvivalent för alla sådana primtal) så att den ℓ-adiska Tℓ av A är . introducerade kriteriet för elliptiska kurvor. Serre och använde resultat av till att utvidga den till abelska varieteter, samt uppkallade resultatet efter Ogg, Néron och (de sade att Oggs resultat verkat vara känt för Sjafarevitj). (sv)
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