Equivariant Chern Classes of Toric Vector Bundles over a DVR and Bruhat--Tits Buildings

Ana María Botero; Kiumars Kaveh; Christopher Manon

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arXiv · 2402.18712

Equivariant Chern Classes of Toric Vector Bundles over a DVR and Bruhat--Tits Buildings

Ana María Botero·Kiumars Kaveh·Christopher Manon

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Abstract

We define equivariant Chern classes of a toric vector bundle over a proper toric scheme over a DVR. We provide a combinatorial description of them in terms of piecewise polynomial functions on the polyhedral complex associated to the toric scheme, which factorize through to an extended Bruhat--Tits building. We further motivate this definition from an arithmetic perspective, connecting to the non-Archimedean Arakelov theory of toric varieties.

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Ana María Botero, Kiumars Kaveh, Christopher Manon. 2024-02-28. Equivariant Chern Classes of Toric Vector Bundles over a DVR and Bruhat--Tits Buildings. https://arxiv.org/abs/2402.18712

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