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We prove that every flat tensor-idempotent in the module category Mod-Tc of a tensor-triangulated category comes from a unique smashing ideal in. We deduce that the lattice of smashing ideals forms a frame. [ABSTRACT FROM AUTHOR]

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the p-local and p-torsion subcategories of the stable category, for each homogeneous prime ideal p in the cohomology ring of the group scheme. [ABSTRACT FROM AUTHOR]

Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category ⊺ equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for ⊺ and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories. [ABSTRACT FROM AUTHOR]

This is a report on recent work of Chałupnik and Touzé. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors. [ABSTRACT FROM PUBLISHER]

We discuss some basic properties of the graded centre of a triangulated category and compute examples arising in representation theory of finite-dimensional algebras. [ABSTRACT FROM PUBLISHER]