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arXiv · 2606.05260

A Counterexample to Bhatt-Lurie's Cohomological Dimension Conjecture

Guo Li
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Abstract

We exhibit a counterexample to a conjecture of Bhatt--Lurie on the cohomological dimension of the Hodge--Tate locus for regular local rings. The example arises from a non-excellent discrete valuation ring constructed by Datta--Smith, closely related to an earlier example of Bosch--L\"{u}tkebohmert--Raynaud. We also explain how the same mechanism yields broader families of counterexamples, while the expected bound is recovered under an excellence hypothesis.

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Guo Li. 2026-06-03. A Counterexample to Bhatt-Lurie's Cohomological Dimension Conjecture. https://arxiv.org/abs/2606.05260

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