An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves
An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves
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相干滑轮的派生类别之间的非傅立叶-穆凯函子的示例
DOI：
10.1007/s00222-019-00862-9
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发表时间：
2019
影响因子：
3.1
通讯作者：
Rizzardo A
中科院分区：
文献类型：
--
作者：
Rizzardo A
Orlov著名的可表征性定理断言在光滑射影变体上相干束的有界派生范畴之间的任何完全忠实的精确函子都是Fourier-Mukai函子。在本文中，我们证明了在没有完全忠实假设的情况下，这个结果是假的。我们也证明了如果地场是，我们的函子不会提升到谱范畴的同伦范畴。
Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier–Mukai functor. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homotopy category of spectral categories if the ground field is.