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HODGE CYCLES AND QUADRATIC RELATIONS BETWEEN HOLOMORPHIC PERIODS ON CM ABELIAN VARIETIES
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 19 September 2025, pp. 1-35
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In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety A, we can construct a CM abelian variety B such that all non-trivial Hodge relations between the holomorphic periods of the product
$A\times B$ are generated by monomial quadratic ones which are also explicit. Moreover, B splits over the Galois closure of the CM field associated with A.
