Weight decomposition for toroidal abelian fibrations

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.

Disclosure

“haripande, Alex Perry, Johannes Schmitt, Pim Spelier, Junliang Shen and Qizheng Yin for helpful discussions. Y.B. is especially grateful to Aaron Pixton for their collaboration, which inspired many of the ideas developed in this paper. Large Language Models were used in the preparation of this manuscript. They helped with image creation, handling the combinatorics and finding typos. The authors have reviewed all of these contributions and maintain full responsibility for the contents of this”

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Classification

Computational experiments or data processing

Multiplier

3

Verified

2026-08-23T05:15:19.084352Z

Structural counts