2,119 research outputs found
The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring
Let R be a commutative ring and let Spec(R) denote the collection of prime
ideals of R. We define a topology on Spec(R) by using ultrafilters and
demonstrate that this topology is identical to the well known patch or
constructible topology. The proof is accomplished by use of a von Neumann
regular ring canonically associated with .Comment: A Remark was added at the end of the paper. To appear in Comm.
Algebr
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
- …