Let $A$ be an abelian variety over a field $F$. Given a field extension $F' \supseteq F$, there is a natural inclusion of endomorphism rings $\End(A)\subseteq\mathrm{End}(A_{F'})$, where $A_{F'}$ denotes the base change of $A$ to $F'$.

Let $K$ be the endomorphism field of $A$. The set of endomorphism rings $\mathrm{End}(A_{F'})$ over subextensions $K \supseteq F' \supseteq F$ forms a lattice under inclusion, called the **endomorphism lattice** of $A$ over $F$.

**Knowl status:**

- Review status: reviewed
- Last edited by John Voight on 2020-09-26 17:05:11

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**History:**(expand/hide all)

- 2020-09-26 17:05:11 by John Voight (Reviewed)
- 2020-09-26 17:05:04 by John Voight
- 2020-09-26 17:03:40 by John Voight
- 2020-09-26 17:03:20 by John Voight
- 2019-05-07 14:46:15 by Christelle Vincent (Reviewed)
- 2019-05-07 14:45:06 by Christelle Vincent
- 2018-05-23 16:38:38 by John Cremona (Reviewed)

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