论文标题
大型科恩·麦克劳（Cohen-Macaulay
Big Cohen-Macaulay test ideals in equal characteristic zero via ultraproducts
论文作者
论文摘要
利用超级副本，Schoutens在本地域$ r $上构建了一个大的Cohen-Macaulay代数$ \ Mathcal {B}（R）$，本质上是$ \ Mathbb {C} $的有限类型的基本上。我们表明，如果$ r $是正常的，并且$δ$是有效的$ \ mathbb {q} $ - $ \ perperatorname {spec} r $ weil divisor，以至于$ k_r+δ$ as $ \ m m mathbb {q} $τ_ {\ hat {\ hat {\ mathcal {b}（r）}}（\ hat {r}，\hatδ）$ of $（\ hat {r}，\hatδ）$相对于$ \ hat {\ hat {\ nathcal {\ nathcal {b}（b}（r）） $（\ hat {r}，\hatδ）$（\ hat {r}，\hatδ）$，其中$ \ hat {r} $和$ \ hat {\ hat {\ mathcal {b}（r）} $ $ \ Mathcal {b}（r）$，$ \hatδ$是规范形态的$δ$的平坦回调，$ \ permatatorm $ \ operatotorname {spec} \ hat {r} \ to \ operatateOrnAme {specorname {spec} r $。作为应用程序，我们获得了纯环扩展下乘数理想的行为的结果。
Utilizing ultraproducts, Schoutens constructed a big Cohen-Macaulay algebra $\mathcal{B}(R)$ over a local domain $R$ essentially of finite type over $\mathbb{C}$. We show that if $R$ is normal and $Δ$ is an effective $\mathbb{Q}$-Weil divisor on $\operatorname{Spec} R$ such that $K_R+Δ$ is $\mathbb{Q}$-Cartier, then the BCM test ideal $τ_{\hat{\mathcal{B}(R)}}(\hat{R},\hatΔ)$ of $(\hat{R},\hatΔ)$ with respect to $\hat{\mathcal{B}(R)}$ coincides with the multiplier ideal $\mathcal{J}(\hat{R},\hatΔ)$ of $(\hat{R},\hatΔ)$, where $\hat{R}$ and $\hat{\mathcal{B}(R)}$ are the $\mathfrak{m}$-adic completions of $R$ and $\mathcal{B}(R)$, respectively, and $\hatΔ$ is the flat pullback of $Δ$ by the canonical morphism $\operatorname{Spec} \hat{R}\to \operatorname{Spec} R$. As an application, we obtain a result on the behavior of multiplier ideals under pure ring extensions.
