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摘要翻译：
我们引入并研究了核代数，即在一个方案的平方上的束范畴中的代数，其中后一范畴通过自然卷积操作具有单体结构。我们证明了许多有趣的范畴，如D-模、等变束及其扭曲形式，都是核代数上模的范畴。我们发展了在这些模范畴之间构造派生等价的技术。作为一个应用，我们推广了Math.AG/9901009关于阿贝尔变体上扭曲微分算子代数上模的结果。作为另一个应用，我们恢复和推广了Laumon在Alg-Geom/9603004中的结果，该结果涉及对偶广义1-动因对上拟相干束的派生范畴的Fourier变换的模拟。
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英文标题：
《Kernel algebras and generalized Fourier-Mukai transforms》
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作者：
Alexander Polishchuk
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最新提交年份：
2008
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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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英文摘要：
We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting categories, such as D-modules, equivariant sheaves and their twisted versions, arise as categories of modules over kernel algebras. We develop the techniques of constructing derived equivalences between these module categories. As one application we generalize the results of math.AG/9901009 concerning modules over algebras of twisted differential operators on abelian varieties. As another application we recover and generalize the results of Laumon in alg-geom/9603004 concerning an analog of the Fourier transform for derived categories of quasicoherent sheaves on a dual pair of generalized 1-motives.
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PDF链接：
https://arxiv.org/pdf/0810.1542
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