If I have two schemes $X$ and $Y$, which are such that my question makes sense (I guess, they should be abelian varieties over a field $k$, so assume this).
Then I have often read, but nowhere found a proper definition, the notion of a $\mathbb{G}_{m}$- biextension of $X \times Y$.
I would be very glad if someone could explain this notion properly to me, maybe with an example (I think one often speaks of the "Poincaré-Biextension).