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arXiv · 1810.07404

Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons

Jeff Achter·Sebastian Casalaina-Martin·Charles Vial
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Abstract

For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles.

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Jeff Achter, Sebastian Casalaina-Martin, Charles Vial. 2019-10-16. Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons. https://doi.org/10.1017/fms.2019.34

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