---
date: 2022-05-14 23:21
modification date: Saturday 14th May 2022 23:21:19
title: "fppf"
aliases: [fppf]
---

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

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [fpqc](fpqc)

---

# fppf

*fidèlement plat de présentation finie*, i.e. a [flat morphism](Unsorted/flat%20morphism.md) [of finite presentation](Unsorted/finitely%20presented.md).
An fppf covering is a covering $T_i\to X$ by flat morphisms which are [locally of finite presentation](Unsorted/finitely%20presented.md).

Needed in order to do [Kummer theory](Unsorted/Kummer%20theory.md) for $p\dash$torsion in characteristic $p$, since the following SES is exact in fppf sheaves but not in etale sheaves:
$$
0\to \mu_p \to \GG_m \mapsvia{\cdot p} \GG_m\to 0
$$