This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
Laszlo and Olsson constructed Grothendieck＇s six operations for constructible complexes on Artin stacks in etale cohomology under an assumption of finite cohomological dimension, with base change established on the l...Laszlo and Olsson constructed Grothendieck＇s six operations for constructible complexes on Artin stacks in etale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. We give a more direct construction of the six operations for complexes on Deligne- Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed by Zheng （2014）. As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and l-adic coefficients.展开更多
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
基金supported by China’s Recruitment Program of Global Experts,National Natural Science Foundation of China(Grant No.11321101)Hua Loo-Keng Key Laboratory of Mathematics,Chinese Academy of Sciences,National Center for Mathematics and Interdisciplinary Sciences and Chinese Academy of Sciences
文摘Laszlo and Olsson constructed Grothendieck＇s six operations for constructible complexes on Artin stacks in etale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. We give a more direct construction of the six operations for complexes on Deligne- Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed by Zheng （2014）. As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and l-adic coefficients.
