{"id":"palomar/PALOMAR-2026-08-22-000010","url":"https://github.com/CBirkbeck/uniform-sheafy-tate-domains-lean/tree/93be0af164d6feec98f17326dd6dcef884751fc9","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-22-000010-v1.json","repo":"https://github.com/CBirkbeck/uniform-sheafy-tate-domains-lean","tags":["math.AG","math.NT","msc:14G22","msc:12J25","msc:13J10","msc:16W80","msc:14G45","rigid-geometry","commutative-algebra","lean-formalization"],"score":0,"title":"CBirkbeck/uniform-sheafy-tate-domains-lean","trust":"high","domain":"math.AG","source":"palomar","authors":["Christopher Birkbeck","Alex Torzewski"],"reviews":0,"subject":"math.AG","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-22","reactions":{},"formalized":true,"formalizes":[{"title":"Uniform sheafy Tate rings that are not stably uniform","identifier":"https://cbirkbeck.github.io/uniform-sheafy-tate-domains/","relationship":"formalizes"}]}