0
votes
2answers
118 views

Poincaré bundle and Weil pairing for Abelian schemes

In which situations is there a Poincaré bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated. The same question for the Weil pairing ...
2
votes
0answers
140 views

When are Abelian schemes projective?

Under what conditions on the base $X$ are Abelian schemes $\mathcal{A}/X$ projective, and projective in which sense?
12
votes
1answer
719 views

Status of Grothendieck's conjecture on homomorphisms of abelian schemes

In [1] Grothendieck posits the following: Conjecture. Let $S$ be a reduced connected scheme, locally of finite type over Spec($\mathbf{Z}$) or a field $k$, $A$ and $B$ two abelian schemes over $S$, ...
1
vote
3answers
410 views

projective subvarieties of the moduli space of abelian varieties

I know that the fibre of $A_{g,n}$ over $\mathbf{F}_p$ is quasi-projective (of what dimension?). Can one exhibit some smooth projective subvarieties of high dimension in it? What are references for ...