The Henselization of a local ring, Part I

Abstract

In the first lecture I will give an introduction to the notion of a Henselian local ring, i.e. a local ring satisfying Hensel's property. Examples are the rings of p-adic integers and formal power series over a field. At the same time I will review several important morphisms in algebraic geometry that rely on Hensel rings, especially quasi-finite and {\'e}tale morphisms. In the second lecture I will focus on the (strict) Henzelization of a local ring, as well as its connection with valuation theory and {\'e}tale topology.