Whether strong sheafiness implies stable uniformity for Tate domains
Follow the latest progress by email.
Must a uniform sheafy Tate Huber pair be stably uniform, meaning that its rational localizations remain uniform? The studied counterexamples impose the stronger sheafiness property as well.
Why it matters and what counts as progress
Why it matters: The implication would reverse the known route from stable uniformity to sheafiness in nonarchimedean geometry.
What counts as progress: A converse theorem or an explicit uniform strongly sheafy Tate domain with a nonuniform rational localization, distinguishing reduced and nonreduced examples.
How the problem developed
- 18 Dec 2015 · Problem statement [1]
Kiran S. Kedlaya Posted Question 7 of the Nonarchimedean Scottish Book: whether a sheafy uniform Tate Huber pair must be stably uniform.
Colin Birkbeck and Patrick Torzewski Released two uniform, strongly sheafy Tate-ring examples that are not stably uniform, with Lean formalizations of the constructions and headline theorems.
AI contribution
AI-origin Tate-domain examples answer a sheafiness question
Birkbeck and Torzewski give uniform, strongly sheafy, nonnoetherian Tate domains that are not stably uniform, answering Kedlaya’s Question 7. One finite-jet example has a nonreduced rational localization; a weighted-parity example has a nonuniform localization that remains a domain.
Sources
- Kedlaya, The Nonarchimedean Scottish Book, Question 7
- Birkbeck and Torzewski, Uniform sheafy Tate rings that are not stably uniform: Lean formalization
- Lean Reservoir package record for UniformSheafyTateDomains
- Uniform sheafy Tate domains: formalization and disclosure
- Birkbeck and Torzewski, Tate-domain paper draft
Website timeline
Publication dates and editorial changes.