发表机构
Universität Hamburg; University of Pennsylvania（汉堡大学; 宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明非交换Grauert定理，推广Fourier-Mukai对偶至广义复环面，建立其导出范畴等价，为广义复膜范畴奠基。
AI 中文摘要
我们证明了一类弯曲微分分次（非交换）Fréchet代数的Grauert高阶凝聚定理的推广。这使得我们能够将Fourier-Mukai演算推广到许多新背景下出现的导出范畴。然后我们应用该定理，并利用Poincaré线丛的非交换版本证明了广义复环面的对偶导出范畴的等价性。这为广义复环面上的广义复膜范畴奠定了基础。例子包括复环面、辛环面以及它们的非交换和B场形变。
英文摘要
We prove a generalization of Grauert's higher coherence theorem for a class of curved differential graded (non-commutative) Fréchet algebras. This allows us to extend the Fourier-Mukai calculus to derived categories arising in many new contexts. We then apply it and prove equivalence of derived categories of dual generalized complex tori using a non-commutative version of the Poincaré line bundle. This lays the foundation for categories of generalized complex branes on generalized complex tori. Examples include complex tori, symplectic tori as well as their non-commutative and B-field deformations.
