# Néron-Severi group

###### Definition 1.

Let $S$ be a surface (an algebraic variety of dimenion $2$) defined over an algebraically closed field $k$. The Néron-Severi group of $S$, denoted by $\operatorname{NS}(S)$, is the group of Weil divisors on $S$ modulo algebraic equivalence of divisors (see parent entry).

###### Theorem (Néron, Severi).

The Néron-Severi group of a surface is a finitely generated abelian group.

Title Néron-Severi group NeronSeveriGroup 2013-03-22 15:34:13 2013-03-22 15:34:13 alozano (2414) alozano (2414) 4 alozano (2414) Definition msc 14C20