6
votes
3answers
549 views

étale cohomology with values in an abelian scheme is torsion?

Let $A/X$ be an abelian scheme. Is $H^n(X,A)$ torsion for $n > 0$? Perhaps this can be proved analogously as Proposition IV.2.7 of Milne's √Čtale cohomology (where it is proved that the ...
3
votes
1answer
310 views

vanishing of étale cohomology groups with small support with values in an abelian scheme

Let $S/k$ be a smooth variety and $A/S$ be an abelian scheme. Let $Z \hookrightarrow S$ be a reduced closed subscheme of codimension $\geq 2$. I want to show that in this situation, $H^i_Z(S, A) = 0$ ...
4
votes
1answer
447 views

A silly question: is the number of points on a Jacobian (of a curve, over a finite field) known?

In a cryptography book I read that people does not known how to compute the number of points on a Jacobian of a hyperelliptic curve $C$ over a finite field $F_q$? Is this true? It seems easy to ...