Abelian varieties, quaternion trick and endomorphisms. (English) Zbl 07828777
Cheltsov, Ivan (ed.) et al., Birational geometry, Kähler-Einstein metrics and degenerations. Proceedings of the conferences, Moscow, Russia, April 8–13, 2019, Shanghai, China, June 10–14, 2019, Pohang, South Korea, November 18–22, 2019. Cham: Springer. Springer Proc. Math. Stat. 409, 857-864 (2023).
Summary: The quaternion trick is an explicit construction that associates to a polarized abelian variety \(X\) a principal polarization of \((X\times X^t)^4\). The aim of this note is to show that this construction is compatible with endomorphisms of \(X\) and \(X^t\). See Theorem 1.1 for a precise statement.
For the entire collection see [Zbl 1515.14010].
For the entire collection see [Zbl 1515.14010].
MSC:
| 14K05 | Algebraic theory of abelian varieties |
References:
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