---
date: 2022-03-29 17:13
modification date: Tuesday 29th March 2022 17:13:04
title: "reduction mod p"
aliases: [reduction mod p]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #AG/schemes 
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# reduction mod p

For $K = \QQ$ and $V \in \Sch\slice{\spec \ZZ}$, reduction $\mod p$ is pulling back:

\begin{tikzcd}
	{X\mod p} && X \\
	\\
	{\spec \FF_p} && {\spec \ZZ}
	\arrow[from=3-1, to=3-3]
	\arrow[from=1-3, to=3-3]
	\arrow[from=1-1, to=3-1]
	\arrow[from=1-1, to=1-3]
	\arrow["\lrcorner"{anchor=center, pos=0.125}, draw=none, from=1-1, to=3-3]
\end{tikzcd}

> [Link to Diagram](https://q.uiver.app/?q=WzAsNCxbMiwwLCJYIl0sWzIsMiwiXFxzcGVjIFxcWloiXSxbMCwyLCJcXHNwZWMgXFxGRl9wIl0sWzAsMCwiWFxcbW9kIHAiXSxbMiwxXSxbMCwxXSxbMywyXSxbMyww**XSxbMywxLCIiLDEseyJzdHlsZSI6eyJuYW1lIjoiY29ybmVyIn19XV0=)


- This works for almost all $p$ and corresponds to reducing the coefficients $\mod p$.