论文标题
同源债券 - 孔定位的理性概念猜想
Homological Bondal-Orlov localization conjecture for rational singularities
论文作者
论文摘要
在特征零字段上，给定理性象y的解决方案$π\ colon \ tilde {x} \ to x $我们使用hodge理论论点来证明函数$ \ mathbf {r} p {r}π_**\ colon \ colon \ colon \ mathbf {d} {d}（dilde）的图像\ Mathbf {d}（x）$之间的有界派生类别的类别生成$ \ mathbf {d}（x）$作为三角形类别。这给出了邦德 - 奥洛夫本地化猜想的薄弱版本，回答了帕维奇和奇德的问题。更普遍地建立了相同的结果，以用于适当的（不必要的异常）形态学$π\ colon \ colon \ tilde {x} \ to x $，并带有$ \ tilde {x} $ smooth，满足$ \ mathbf {r}π_*（r}π_*） \ Mathcal {O} _x $。
Given a resolution of rational singularities $π\colon \tilde{X} \to X$ over a field of characteristic zero we use a Hodge-theoretic argument to prove that the image of the functor $\mathbf{R}π_*\colon \mathbf{D}(\tilde{X}) \to \mathbf{D}(X)$ between bounded derived categories of coherent sheaves generates $\mathbf{D}(X)$ as a triangulated category. This gives a weak version of the Bondal-Orlov localization conjecture, answering a question of Pavic and Shinder. The same result is established more generally for proper (non-necessarily birational) morphisms $π\colon \tilde{X} \to X$, with $\tilde{X}$ smooth, satisfying $\mathbf{R}π_*(\mathcal{O}_{\tilde{X}}) = \mathcal{O}_X$.
