Grothendieck-Neeman duality and the Wirthm\"uller isomorphism

We clarify the relationship between Grothendieck duality \`a la Neeman and the Wirthm\"uller isomorphism \`a la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated tensor-triangulated categories, which leads to a surprising trichotomy: There exist either exactly three adjoints, exactly five, or infinitely many. We highlight the importance of so-called relative dualizing objects and explain how they give rise to dualities on canonical subcategories. This yields a duality theory rich enough to capture the main features of Grothendieck duality in algebraic geometry, of generalized Pontryagin-Matlis duality \`a la Dwyer-Greenlees-Iyengar in the theory of ring spectra, and of Brown-Comenetz duality \`a la Neeman in stable homotopy theory.Comment: 36 pages. Minor revision due to referee's comments. Added Examples 3.27, 4.8 & 4.9. To appear in Compositio Mat

Cohomological Mackey 2-functors

We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in arXiv:1808.04902, obtained by modding out the so-called cohomological relations. This categorifies Yoshida's Theorem for ordinary cohomological Mackey functors, and provides a direct connection between Mackey 2-motives and the usual blocks of representation theory.Comment: 27 page

Sustainable consumption: towards action and impact. : International scientific conference November 6th-8th 2011, Hamburg - European Green Capital 2011, Germany: abstract volume

This volume contains the abstracts of all oral and poster presentations of the international scientific conference „Sustainable Consumption – Towards Action and Impact“ held in Hamburg (Germany) on November 6th-8th 2011. This unique conference aims to promote a comprehensive academic discourse on issues concerning sustainable consumption and brings together scholars from a wide range of academic disciplines. In modern societies, private consumption is a multifaceted and ambivalent phenomenon: it is a ubiquitous social practice and an economic driving force, yet at the same time, its consequences are in conflict with important social and environmental sustainability goals. Finding paths towards “sustainable consumption” has therefore become a major political issue. In order to properly understand the challenge of “sustainable consumption”, identify unsustainable patterns of consumption and bring forward the necessary innovations, a collaborative effort of researchers from different disciplines is needed

On the derived category of a graded commutative noetherian ring

For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijection between, on the one hand, the twist-closed localizing subcategories of the derived category, and, on the other hand, subsets of the homogeneous spectrum of prime ideals of the ring. We provide an application to weighted projective schemes.Comment: 19 pages; minor corrections, added a few detail

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories