# Néron-Severi group

###### Definition 1.

Let $S$ be a surface (an algebraic variety of dimenion $\mathrm{2}$) defined over an algebraically closed field $k$. The Néron-Severi group of $S$, denoted by $\mathrm{NS}\mathit{}\mathrm{(}S\mathrm{)}$, 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 |
---|---|

Canonical name | NeronSeveriGroup |

Date of creation | 2013-03-22 15:34:13 |

Last modified on | 2013-03-22 15:34:13 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 4 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 14C20 |