### Irreducible components of rigid spaces

This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field $k$. We prove the excellence of the local rings on rigid spaces over $k$. This is used to prove the standard existence theorems and to show compatibility with the notion of irreducible components for schemes and formal schemes. Behavior with respect to extension of the base field is also studied. It is often necessary to augment scheme-theoretic techniques with other algebraic...