On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings

By J. Št’ovíček, David Pospíšil. 2012

47 citations recorded by the source corpus.

We classify compactly generated co-t-structures on the derived category of a commutative noetherian ring. In order to accomplish that, we develop a theory for compactly generated Hom-orthogonal pairs (also known as torsion pairs in the literature) in triangulated categories that resembles Bousfield localization theory. Finally, we show that the category of perfect complexes over a connected commutative noetherian ring admits only the trivial co-t-structures and (de)suspensions of the canonical co-t-structure and use this to describe all silting objects in the category.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aca9b89e7496384e7e7d2496b7e6d5ccd85eddfa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

J. Št’ovíček

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Torsion pairs in silting theory (2016, unknown): “If T is moreover an algebraic triangulated category, then such a pair admits a right adjacent torsion pair, as shown in [Št ´ ovíˇcek and Pospíšil 2016, Theorem 3.11].”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “Exact categories of Grothendieck type In various contexts (see [65, 68] for example), it is useful to consider more general categories than Grothendieck categories.”