Weight decomposition for toroidal abelian fibrations

Younghan Bae; Jeremy Feusi; Aitor Iribar Lopez; Sam Molcho

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arXiv · 2608.14337

Weight decomposition for toroidal abelian fibrations

Younghan Bae·Jeremy Feusi·Aitor Iribar Lopez·Sam Molcho

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Abstract

We study the action of the rational multiplication by $N$ map on the Chow groups of degenerations of principally polarized abelian varieties of torus rank at most one, as well as its interaction with the Fourier transform. As applications, we compute the class of the unit section, prove a generalized weight decomposition of the relative Chow motive of the universal family of such degenerations, and completely determine its tautological ring.

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Younghan Bae, Jeremy Feusi, Aitor Iribar Lopez, Sam Molcho. 2026-08-14. Weight decomposition for toroidal abelian fibrations. https://arxiv.org/abs/2608.14337

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