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JOURNALS // Moscow Mathematical Journal // Archive

Mosc. Math. J., 2004 Volume 4, Number 2, Pages 503–510 (Mi mmj157)

This article is cited in 1 paper

Theta groups over extensions of abelian varieties by unipotent groups

F. Pablos Romo

University of Salamanca

Abstract: Let $0\to K_U\overset i\to Y\overset\pi\to X\to 0$ be a sequence of morphisms of algebraic groups over an algebraically closed field $k$, where $X$ is an abelian variety, $K_U$ is a unipotent, connected and commutative group scheme, and $(X,\pi)$ is a geometric quotient of $Y$ by $K_U$.
If $\mathcal L$ is an invertible sheaf over $X$, in this paper we generalize to $\overline{\mathcal L}=\pi^*\mathcal L$ the notion of a theta group associated with an invertible sheaf given by $D$. Mumford for an abelian variety.

Key words and phrases: Theta group, invertible sheaf, unipotent group, abelian variety.

MSC: 14K05, 14K30, 14L15

Received: May 6, 2002

Language: English

DOI: 10.17323/1609-4514-2004-4-2-503-510



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