MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For elliptic curve $E$ defined over $K_v$ we know that $E(K_v)$ = $Z_p^{[K_v:Q_p]} + T$(direct sum) where v is prime of K above p and T is finite abelian group(By prop 6.3 in Silverman's book). In the proof of that proposition, Silverman used Formal Group.
My question is that it is still true for Jacobian of (hyperelliptic) curve of genus g larger than 1?

In other words, $J(C)(K_v) = Z_p^{g[K_v:Q_p]} + T$(direct sum) holds?

Thank you in advance.

share|cite|improve this question
A. Mattuck, Abelian varieties over p-adic ground fields, Ann. Math. 62 (1955) 92-119. – Felipe Voloch Aug 26 '13 at 0:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.