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arXiv · 2503.12835

Tropical Poincar\'e bundle, Fourier-Mukai transform, and a generalized Poincar\'e formula

Soham Ghosh·Farbod Shokrieh
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Abstract

We construct a tropical analogue of the Poincar\'e bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincar\'e formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theorem for tropical abelian varieties, as well as a tropical Poincar\'e-Prym formula which was recently conjectured by R\"ohrle and Zakharov.

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Soham Ghosh, Farbod Shokrieh. 2025-03-17. Tropical Poincar\'e bundle, Fourier-Mukai transform, and a generalized Poincar\'e formula. https://arxiv.org/abs/2503.12835

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