Reconstructing the spectrum of F_1 from the stable homotopy category

Details Reconstructing the spectrum of F_1 from the stable homotopy category Reconstructing the spectrum of F_1 from the stable homotopy category

2011-03-07

arxiv.org/abs/1103.1235v3

Mathematics

Algebraic Geometry

Scientific paper

The finite stable homotopy category S_0 has been suggested as a candidate for a category of perfect complexes over the monoid scheme Spec F_1. We apply a reconstruction theorem from algebraic geometry to S_0, and show that one recovers the one point topological space. We also classify filtering subsets of the set of principal thick subcategories of S_0, and of its p-local versions. This is motivated by a result saying that the analogous classification for the category of perfect complexes over an affine scheme provides topological information.

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