2024/03/12 by Mikhail V. Bondarko, Bondarko, Mikhail V.
Computer Science · Engineering · #14A15 #14F08 (Primary) 18F20 #14G40 (Secondary) #18E10 #18G05 #18G80 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Optimization and Variational Analysis #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2403.07855
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study t-structures (on triangulated categories) that are closely related to weight structures. A t-structure couple t=(Ct≤ 0,Ct≥ 0) is said to be adjacent to a weight structure w=(Cw≤ 0, Cw≥ 0) if Ct≥ 0=Cw≥ 0. For a category C that satisfies the Brown representability property we prove that t that is adjacent to w exists if and only if w is smashing (that is, "respects C-coproducts"). The heart Ht of this t is the category of those functors Hwop→ Ab that respect products (here Hw is the heart of w); the result has important applications. We prove several more statements on constructing t-structures starting from weight structures; we look for a strictly orthogonal t-structure t on some C' (where C,C' are triangulated subcategories of a common D) such that C't≤ 0 (resp. C't≥ 0) is characterized by the vanishing of morphisms from Cw≥ 1 (resp. Cw≤ -1). Some of these results generalize properties of semi-orthogonal decompositions proved in the previous paper, and can be applied to various derived categories of (quasi)coherent sheaves on a scheme X that is projective over an affine noetherian one. We also study hearts of orthogonal t-structures and their restrictions, and prove some statements on "reconstructing" weight structures from orthogonal t-structures.