The ST correspondence for proper non-positive dg algebras

2021/05/10 by Houjun Zhang, Zhang, Houjun
Mathematics · Physics and Astronomy · #16E35 #16E45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.CT #math.RT #msc:16E35 #msc:16E45

paper · pdf · doi:10.48550/arxiv.2105.04095

arxiv created 2021/05/10 · openalex publication_date 2021/05/10 · arxiv updated 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 D_fd(A), we construct a 'dual' silting object of the perfect derived category 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 per(A) and algebraic t-structures of D_fd(A).

Related

• The correspondence between silting objects and t-structures for non-positive dg algebras
• From simple-minded collections to silting objects via Koszul duality
• Koszul differential graded algebras and BGG correspondence
• Contravariant Koszul duality between non-positive and positive dg algebras
• Derived equivalences induced by good silting complexes