Finiteness of global dimension relative to compact silting objects is intrinsic to the triangulated category and independent of the silting object chosen.
Finiteness of homological dimensions in triangulated categories
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate the finitistic, big finitistic, and global dimensions, and establish explicit inequalities that relate these dimensions of the middle category in a recollement of triangulated categories to those of the outer categories. This provides a unified framework for extending some known results on the homological dimensions of ordinary rings to weakly approximable triangulated categories.
fields
math.RT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Global dimension of dg algebras via compact silting objects
Finiteness of global dimension relative to compact silting objects is intrinsic to the triangulated category and independent of the silting object chosen.