10,034 research outputs found
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
The basic geometry of Witt vectors, I: The affine case
We give a concrete description of the category of etale algebras over the
ring of Witt vectors of a given finite length with entries in an arbitrary
ring. We do this not only for the classical p-typical and big Witt vector
functors but also for variants of these functors which are in a certain sense
their analogues over arbitrary local and global fields. The basic theory of
these generalized Witt vectors is developed from the point of view of commuting
Frobenius lifts and their universal properties, which is a new approach even
for the classical Witt vectors. The larger purpose of this paper is to provide
the affine foundations for the algebraic geometry of generalized Witt schemes
and arithmetic jet spaces. So the basics here are developed somewhat fully,
with an eye toward future applications.Comment: Final versio
tt-geometry of Tate motives over algebraically closed fields
We study Tate motives with integral coefficients through the lens of tensor
triangular geometry. For some base fields, including the field of algebraic
numbers and the algebraic closure of a finite field, we arrive at a complete
description of the tensor triangular spectrum and a classification of thick
tensor ideals.Comment: 38 pages; v3: completes description of structure sheaf on
tt-spectrum; v4: final accepted versio
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