Reduction and lifting problem for differential forms on Berkovich curves

Michael Temkin*, Ilya Tyomkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a complete real-valued field k of residue characteristic zero, we study properties of a differential form ω on a smooth proper k-analytic curve X. In particular, we associate to (X,ω) a natural tropical reduction datum combining tropical data of (X,ω) and algebra-geometric reduction data over the residue field k˜. We show that this datum satisfies natural compatibility condition, and prove a lifting theorem asserting that any compatible tropical reduction datum lifts to an actual pair (X,ω). In particular, we obtain a short proof of the main result of [2].

Original languageAmerican English
Article number108208
JournalAdvances in Mathematics
StatePublished - 5 Mar 2022

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  • Berkovich spaces
  • Differential forms
  • Stable reduction


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