The spectrum of the equivariant stable homotopy category of a finite group

We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in determining its topology and obtain a complete answer for groups of square-free order. For general finite groups, we describe the topology up to an unresolved indeterminacy, which we reduce to the case of p-groups. We then translate the remaining unresolved question into a new chromatic blue-shift phenomenon for Tate cohomology. Finally, we draw conclusions on the classification of thick tensor ideals.Comment: 34 pages, to appear in Invent. Mat

Morphological design control for large-scale city development: A new proposal

Whereas many good examples can be found of the study of urban morphology informing the design of new residential areas in Europe, it is much more difficult to find examples relating to other land uses and outside of Europe. This paper addresses a particular issue, the control and coordination of large and complex development schemes within cities, and, in doing so, considers commercial and mixed-use schemes outside of Europe. It is argued that urban morphology has much to offer for both the design of such development and its implementation over time. Firstly, lessons are drawn from the work of Krier and Rossi in Berlin, the form-based guidance developed in Chelmsford, UK, and the redesign and coordination of the Melrose Arch project in Johannesburg, SA. A recent development at Boggo Road in Brisbane, Australia, is then subjected to a more detailed examination. It is argued that the scheme has been unsatisfactory in terms of both design and implementation. An alternative framework based on historical morphological studies is proposed that would overcome these deficiencies. It is proposed that this points the way to a general approach that could be incorporated within the planning process internationally