# Tagged Questions

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**2**answers

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### Poincaré bundle and Weil pairing for Abelian schemes

In which situations is there a PoincarĂ© bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated.
The same question for the Weil pairing ...

**2**

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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?

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### 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 $S$, ...

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**3**answers

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 ...