Bhatt–Lurie’s cohomological dimension conjecture for the Hodge–Tate locus

Let $R$ be a $p$-complete noetherian regular local ring with perfect residue field. The Hodge–Tate locus is denoted by $\operatorname{WCart}^{\mathrm{HT}}_{\operatorname{Spf}(R)}$, and $\operatorname{R\Gamma}(\operatorname{WCart}^{\mathrm{HT}}_{\operatorname{Spf}(R)},-)$ denotes derived global sections.

Bhatt–Lurie’s cohomological dimension conjecture. The functor

$$\operatorname{R\Gamma}(\operatorname{WCart}^{\mathrm{HT}}_{\operatorname{Spf}(R)},-)$$

carries $\mathcal{D}^{\leq 0}$ to $\mathcal{D}^{\leq \dim(R)}$.

The conjecture predicts a cohomological-dimension bound for the Hodge–Tate locus of a regular local ring. The source paper’s title and abstract state that it exhibits a counterexample, so the conjecture is refuted in the generality stated; the expected bound is recovered under an excellence hypothesis.