Abstract
In Chapter 1 we saw that the ring of endomorphisms End(X) of a complex torus X is a free abelian group of finite rank. This implies that End ℚ(X) is a finite dimensional ℚ-algebra. If moreover X is an abelian variety, any polarization L induces an anti-involution f ↦ f′ on End ℚ(X), called the Rosati involution. It is the adjoint operator with respect to the hermitian form c 1 (L).
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© 2004 Springer-Verlag Berlin Heidelberg
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Birkenhake, C., Lange, H. (2004). Endomorphisms of Abelian Varieties. In: Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften, vol 302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06307-1_7
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DOI: https://doi.org/10.1007/978-3-662-06307-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05807-3
Online ISBN: 978-3-662-06307-1
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