---
date: 2022-03-17 20:41
modification date: Thursday 17th March 2022 21:00:18
title: Serre-Tate theory
aliases: [Serre-Tate theory]

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- Tags 
	- #todo/untagged
- Refs:
	- <https://arxiv.org/abs/1807.11295>
- Links:
	- #todo/create-links 

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# Serre-Tate theory
![](attachments/Pasted%20image%2020220317204119.png)

As an important step in his proof of the [Tate conjecture](Tate%20conjecture.md) for ordinary [K3 surfaces](K3%20surfaces.md), Nygaard has developed an appropriate version of Serre-Tate theory. His results were recently extended to [Calabi-Yau](Calabi-Yau.md) threefolds by Ward in his thesis [War14]. In fact, the same methods can be used to yield an analog for higher-dimensional varieties, under some extra assumptions.

See [Hodge polygon](Hodge%20polygon.md)