AI 中文总结
该研究证明了满足特定条件的射影态射下导出前推的等价关系，并由此得到拟射影三维代数簇的邦达尔-奥尔洛夫局部化猜想的无特征形式，推进了代数几何中导出范畴的相关猜想研究。
AI 中文摘要
设X为具有分解性质的诺特概形，p:Y→X为射影态射，假设对i>2有R^i p_*=0，且O_X→Rp_*O_Y为同构。我们证明导出前推诱导出等价关系D^b(Y)/Ker(Rp_*)≃D^b(X)。作为应用，我们证明了拟射影三维代数簇的邦达尔-奥尔洛夫局部化猜想的无特征形式。
英文摘要
Let $X$ be a noetherian scheme with the resolution property, and let $p:Y\to X$ be a projective morphism. Suppose that $R^{i}p_{*}=0$ for $i>2$ and that $ \mathcal {O}_{X}\longrightarrow Rp_{*}\mathcal {O}_{Y} $ is an isomorphism. We show that derived pushforward induces an equivalence \[ D^{b}(Y)/\operatorname{Ker}(Rp_{*})\simeq D^{b}(X). \] As an application, we prove a characteristic-free form of the Bondal--Orlov localization conjecture for quasi-projective threefolds.
