The ST correspondence for proper non-positive dg algebras

Abstract

Let A be a proper non-positive dg algebra over a field k. For a simple-minded collection of the finite-dimensional derived category ${\mathcal{D}}_{fd}(A)$, we construct a “dual” silting object of the perfect derived category $\text{per}(A)$ by using the Koszul duality for dg algebras. This induces a one-to-one correspondence between the equivalence classes of silting objects in $\text{per}(A)$ and algebraic t-structures of ${\mathcal{D}}_{fd}(A)$.

Keywords:

• Differential graded algebra
• simple-minded collection
• silting object
• ST correspondence

2020 Mathematics Subject Classification:

• 16E35
• 16E45

Acknowledgments

The author would like to thank Dong Yang for introducing me this topic and for his consistent encouragement and support. He also thanks Zongzhen Xie for her careful reading of the paper and for her helpful comments.

Additional information

Funding

The project is funded by China Postdoctoral Science Foundation (2020M681540).