---
date: 2022-04-17 01:34
modification date: Sunday 17th April 2022 01:34:08
title: "geometrically connected"
aliases: [geometrically connected]
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# geometrically connected

Idea: [base change](base%20change.md) can disconnect a connected scheme, but not if it's geometrically connected.

- $X \in \Sch\slice k$ is **geometrically connected** iff $X\fiberprod{k} L$ is connected for every field extension $k\injects L$.