Base change for semiorthogonal decompositions
Base change for semiorthogonal decompositions
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DOI：
10.1112/s0010437x10005166
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发表时间：
2007-11
影响因子：
1.8
通讯作者：
A. Kuznetsov
中科院分区：
文献类型：
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作者：
A. Kuznetsov
设X是基概型S上的代数簇，T→S是基变换。给定X上凝聚层的有界导出范畴B（X）中的一个容许子范畴Xb，在一定的技术条件下，我们构造了B（X×ST）中的一个容许子范畴Xb T，称为Xb的基变换，使得基变换定理成立：如果B（X）的一个半正交分解被给定，则其分支的基变换构成B（X×ST）的一个半正交分解.𝒟𝒟𝒟𝒟作为中间步骤，我们构造了X上拟相干层的无界导出范畴和X上完全复形范畴的半正交分解的相容系统。作为应用，我们证明了半正交分解的投影函子是核函子。
Abstract Let X be an algebraic variety over a base scheme S and ϕ:T→S a base change. Given an admissible subcategory 𝒜 in 𝒟b(X), the bounded derived category of coherent sheaves on X, we construct under some technical conditions an admissible subcategory 𝒜T in 𝒟b(X×ST), called the base change of 𝒜, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of 𝒟b (X) is given, then the base changes of its components form a semiorthogonal decomposition of 𝒟b (X×ST) . As an intermediate step, we construct a compatible system of semiorthogonal decompositions of the unbounded derived category of quasicoherent sheaves on X and of the category of perfect complexes on X. As an application, we prove that the projection functors of a semiorthogonal decomposition are kernel functors.