Algebre commutative et introduction a geometrie algebrique

Chambert-Loir A.

This graduate course has two faces: algebra and geometry. Indeed, we study simultaneously loci of points defined by polynomial equations and algebras of finite type over a field. We shall show on examples (Hilbert’s Nullstellensatz, dimension theory, regularity) how these are two faces of a single head and how both geometrie and algebraic aspects enlight the one the other.