nLab
integral scheme

Contents

Definition

An algebraic scheme XX is integral if for any Zariski open subset UXU\subset X the ring of sections 𝒪 X(U)\mathcal{O}_X(U) of the structure sheaf over UU is an integral domain.

Properties

Equivalent characterizations

A scheme is integral iff it is both reduced and irreducible. Integral schemes of finite type over the spectrum of an algebraically closed field correspond (in the sense of equivalence of categories) to classical algebraic varieties.

Revised on May 30, 2013 12:54:48 by Urs Schreiber (82.113.121.121)