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Irreducible components of rigid spaces

Brian Conrad (1999)

Annales de l'institut Fourier

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...

On topological classification of complex mappings

Hadi Seyedinejad, Ali Zaghian (2015)

Annales Polonici Mathematici

We study the topological invariant ϕ of Kwieciński and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for ϕ of a general mapping, which is similarly effective as the upper bound given by Kwieciński and Tworzewski. Some classes of mappings are identified for which the exact value of ϕ can be computed. Also, we prove that the variation of ϕ on the source space of a mapping with a smooth target is semicontinuous in the Zariski topology.

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