The Decomposition, Inertia and Ramification Groups in Birational Geometry

Abstract

Let X be an irreducible scheme, let Bir(X) be its group of birational automorphisms, let G be a subgroup of Bir(X). If g ∈ G, then dom(g) denotes the domain of definition of the map g, g* denotes the corresponding automorphism of the total ring of fractions on X. Let Y be an irreducible reduced subscheme of X, let p _y be the generic point of Y, let A _y be the local ring of p _y , let m _y be the maximal ideal of A _y .