Open Research Index

CBirkbeck/uniform-sheafy-tate-domains-lean

Christopher Birkbeck, Alex Torzewski

Palomar Registrypalomar/PALOMAR-2026-08-22-000010Aug 22, 2026math.AGscore 0

A Lean 4 formalisation of *Uniform sheafy Tate rings that are not stably uniform* (Birkbeck–Torzewski), answering Question 7 of Kedlaya's *Nonarchimedean Scottish Book* in the negative: a sheafy uniform Huber pair need not be stably uniform. Buzzard–Verberkmoes and Mihara proved that stably uniform Tate Huber rings are sheafy; whether the converse holds was open. The paper gives two complete Tate algebras over a complete discretely valued field `k` that are uniform, nonnoetherian integral domains with `A° = A₀`, strongly sheafy (every Tate algebra `A⟨X₁, …, Xₙ⟩` is sheafy), and yet not…

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