Inheritance of local topological properties of schemes

TL;DR

This paper demonstrates that certain local topological properties of schemes are preserved under specific types of morphisms, such as locally quasi-finite, flat, and locally finitely presented maps.

Contribution

It establishes that properties like being locally topologically noetherian, locally connected, or having finitely many irreducible components are inherited under these morphisms.

Findings

Preservation of local topological properties under specific morphisms

Examples include locally topologically noetherian and locally connected schemes

Inheritance of properties like finitely many irreducible components

Abstract

This paper shows that for certain local topological properties, given a locally quasi-finite, flat and locally finitely presented map of schemes $f\colon X\to Y$, if $Y$ has the property, then so does $X$. We also show that being locally topologically noetherian or locally connected or having locally finitely many irreducible components are examples for these local topological properties.