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摘要翻译：
考虑一个代数变体$x$在一个基方案$s$和一个忠实的基更改$t\到s$上。给定$x$上相干束的有界导出范畴中的一个可容许子范畴$\ca$,我们构造了纤维积$x\times_sT$上相干束的有界导出范畴中的一个可容许子范畴，称为$\ca$的基变，其基变定理成立：如果给出$x$的有界导出范畴的半拓扑分解，则其分量的基变构成纤维积的有界导出范畴的半拓扑分解。作为中间步骤，我们构造了$x$上拟合束的无界导出范畴和$x$上完全复形范畴的半正交分解的相容系统。作为应用，我们证明了半三角分解的投影函子是核函子。
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英文标题：
《Base change for semiorthogonal decompositions》
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作者：
Alexander Kuznetsov
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Category Theory 范畴理论
分类描述：Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
丰富范畴，topoi，abelian范畴，monoidal范畴，同调代数
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英文摘要：
Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \to S$. Given an admissible subcategory $\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the bounded derived category of coherent sheaves on the fiber product $X\times_S T$, called the base change of $\CA$, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of the bounded derived category of $X$ is given then the base changes of its components form a semiorthogonal decomposition of the bounded derived category of the fiber product. 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.
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PDF链接：
https://arxiv.org/pdf/0711.1734
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