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arXiv · 2509.12167

Log geometry and lifting rational points

Leo Herr·Sara Mehidi·Marta Pieropan·Thibault Poiret
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Abstract

For a morphism $f : X \to Y$ of schemes, we give a tropical criterion for which points of $Y$ (valued in a field, discrete valuation ring, number ring, or Dedekind domain) lift to $X$. Our criterion extends the firmaments of Abramovich to a wide range of morphisms, even logarithmic stable maps.

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Leo Herr, Sara Mehidi, Marta Pieropan, Thibault Poiret. 2025-09-15. Log geometry and lifting rational points. https://arxiv.org/abs/2509.12167

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