Functors given by kernels, adjunctions and duality
Functors given by kernels, adjunctions and duality
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由核、附加物和对偶性给出的函子
DOI：
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发表时间：
2013
期刊：
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通讯作者：
D. Gaitsgory
中科院分区：
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作者：
D. Gaitsgory
设X_1和X_2是特征为0的域上的有限型格式。设Q是范畴D-mod(X_1\×X_2)中的一个对象，考虑由Q定义的函子F：D-mod(X_1)->；Dmod(X_2)，假设F在D-mod(X_1\×X_2)中有一个也由对象P定义的右伴随.本文提出和回答的问题是P如何与Q的Verdier对偶有关，我们随后将这个问题推广到当X_1和X_2不再是方案而是Artin堆栈的情况，在这种情况下变得更加有趣。
Let X_1 and X_2 be schemes of finite type over a field of characteristic 0. Let Q be an object in the category D-mod(X_1\times X_2) and consider the functor F:D-mod(X_1)->Dmod(X_2) defined by Q. Assume that F admits a right adjoint also defined by an object P in D-mod(X_1\times X_2). The question that we pose and answer in this paper is how P is related to the Verdier dual of Q. We subsequently generalize this question to the case when X_1 and X_2 are no longer schemes but Artin stacks, where the situation becomes much more interesting.