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 …

The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D.
Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of …

The cohomology annihilator of a noetherian ring that is finitely generated as a module over
its center is introduced. Results are established linking the existence of nontrivial …

We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …

The mono-epi (ME) exact structure on the morphisms of an exact category is introduced and
used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and …

Hochschild Dimensions of Tilting Objects Page 1 M. Ballard and D. Favero (2012) “Hochschild
Dimensions of Tilting Objects,” International Mathematics Research Notices, Vol. 2012, No. 11 …

We provide an axiomatic approach for studying support varieties of objects in a triangulated
category via the action of a tensor triangulated category, where the tensor product is not …

From the viewpoint of higher dimensional Auslander–Reiten theory, we introduce a new
class of finite dimensional algebras of global dimension n, which we call n-representation …

Several years ago, Bondal, Rouquier, and Van den Bergh introduced the notion of the
dimension of a triangulated category, and Rouquier proved that the bounded derived …

We advance support variety theory for finite tensor categories. First we show that the
dimension of the support variety of an object equals the rate of growth of a minimal …