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arXiv · 2601.13277

On surfaces with smooth projective models over $\mathbb{Z}$

Fabio Bernasconi·Gebhard Martin·Zsolt Patakfalvi
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Abstract

In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their arithmetic and cohomological invariants. Along the way we collect some results on smooth projective models of surfaces over Dedekind domains.

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Fabio Bernasconi, Gebhard Martin, Zsolt Patakfalvi. 2026-01-19. On surfaces with smooth projective models over $\mathbb{Z}$. https://arxiv.org/abs/2601.13277

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