Korean J. Math. Vol. 30 No. 3 (2022) pp.555-560
DOI: https://doi.org/10.11568/kjm.2022.30.3.555

Restriction of scalars with simple endomorphism algebra

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Hoseog Yu


Suppose $L/K$ be a finite abelian extension of number fields of odd degree and suppose an abelian variety $A$ defined over $L$ is a $K$-variety. If the endomorphism algebra of $A/L$ is a field $F$, the followings are equivalent : 
(1) The enodomorphiam algebra of the restriction of scalars from $L$ to $K$ is simple. 
(2) There is no proper subfield of $L$ containing $L^{G_F}$ on which $A$ has a $K$-variety descent.

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