Skip to main content
2 of 4
added 16 characters in body
Anweshi
  • 7.4k
  • 11
  • 75
  • 99

Torsion of an abelian variety under reduction.

Let $p$ be a prime. Suppose you have an Abelian scheme $A$ over $Spec\ \mathbb{Z}_p$. Suppose it has good reduction $A_p$. How do you prove that if $q$ is another prime, then the $q$-torsion of $A$ injects into the torsion of $A_p$, under the reduction map?

Anweshi
  • 7.4k
  • 11
  • 75
  • 99