Log geometry and lifting rational points

Published 15 Sep 2025 in math.AG and math.NT | (2509.12167v1)

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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