The ST correspondence for proper non-positive dg algebras

TL;DR

This paper establishes a correspondence between silting objects and algebraic t-structures in the derived categories of proper non-positive dg algebras using Koszul duality.

Contribution

It constructs a dual silting object from simple-minded collections and proves a bijective correspondence with algebraic t-structures.

Findings

Constructs dual silting objects from simple-minded collections.

Establishes a one-to-one correspondence between silting objects and algebraic t-structures.

Utilizes Koszul duality for 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 $\mathrm{per}(A)$ by using the Koszul duality for dg algebras. This induces a one-to-one correspondence between the equivalence classes of silting objects in $\mathrm{per}(A)$ and algebraic t-structures of $\mathcal{D}_{fd}(A)$.