# Compactification of degenerate abelian schemes over a regular divisor

### Sandra Rozensztajn

LAGA, Institut Galilée Université Paris 13 99 avenue J.-B. Clément, 94340 Villetaneuse, France

## Abstract

We consider a semiabelian scheme $G$ over a regular base scheme $S$, which is generically abelian, such that the points of the base where the scheme is not abelian form a regular divisor $S_{0}$. We construct a compactification of $G$, that is a proper flat scheme $P$ over the base scheme, containing $G$ as a dense open set, such that $P_{S_{0}}$ is a divisor with normal crossings in $P$. We also show that given an isogeny between two such semiabelian schemes, we can construct the compactifications so that the isogeny extends to a morphism between the compactifications.

## Cite this article

Sandra Rozensztajn, Compactification of degenerate abelian schemes over a regular divisor. Doc. Math. 11 (2006), pp. 57–71

DOI 10.4171/DM/204