Regulärer Ring/Positive Charakteristik/Erzwingende Algebra/Nicht drin/Lokale Kohomologie/en/Fakt

Let $(R, 𝔪)$ denote a regular local ring of dimension $d$ and of positive characteristic, let $I = (f_{1}, \dots, f_{n})$ be an $𝔪$ -primary ideal and $f \in R$ be an element with $f \notin I$ . Let $B = R [T_{1}, \dots, T_{n}] / (f_{1} T_{1} + \dots + f_{n} T_{n} + f)$ be the corresponding forcing algebra.

Then the extended ideal $𝔪 B$ satisfies

$H_{𝔪 B}^{d} (B) = H^{d - 1} (D (𝔪 B), 𝒪_{B}) = 0 .$

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