We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived
scheme or Artin stack, where “quasi-smooth” means that it is a locally complete intersection …

arXiv:0806.1324v2 [math.CT] 14 Mar 2009 Page 1 arXiv:0806.1324v2 [math.CT] 14 Mar 2009
LOCALIZATION THEORY FOR TRIANGULATED CATEGORIES HENNING KRAUSE Contents …

We classify localising subcategories of the stable modulde category of the finite group that
are closed under tensor product with simple (or, equivalently all) modules. One application …

Tensor triangular geometry Page 1 Proceedings of the International Congress of Mathematicians
Hyderabad, India, 2010 Tensor triangular geometry Paul Balmer∗ Abstract. We survey tensor …

We construct a natural continuous map from the triangular spectrum of a tensor triangulated
category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We …

We systematically develop a theory of stratification in the context of tensor triangular
geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral …

We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

We transpose Rickard's construction of idempotent representations to the general context of
tensor triangulated categories. We connect our construction to the telescope conjecture and …

A notion of stratification is introduced for any compactly generated triangulated category⊤
endowed with an action of a graded‐commutative noetherian ring R. The utility of this notion …