##  [Pathological Base Change](/pathological-base-change) 

  ##  [Pathological Base Change](https://algebra.quantumdictionary.io/pathological-base-change-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A phenomenon where a natural formation (normalization, formation of fibers, higher direct images, schematic closure, etc.) does not commute with base change along a morphism of schemes, producing unexpected or ill-behaved fibers or breaking properties expected to be preserved under change of base.