Inheritance of local topological properties of schemes

2024/11/12 by Gramzow, Johann
#14A15 (Primary) #14B25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.08252

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→ 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.

Related

• Local structure theorems for smooth maps of formal schemes
• Finiteness of cohomology for pro-locally proper maps
• Schemes as functors on topological rings
• Local systems which do not come from abelian varieties
• Reconstruction of schemes from their étale topoi