PreprintCC BY 4.0arXiv
Rational torus equivariant spectra VII: the Cousin complex
Abstract
We explore the analogy between rational G-spectra for an r-torus G and sheaves over an r-dimensional scheme, in the context of the author's algebraic model for rational G-spectra. In particular, the resolution of the sphere of a virtual representation in the standard model corresponds precisely to the Cousin complex resolution of a line bundle. The tom Dieck splitting for the sphere of an actual respresentation corresponds to the collapse of the Cousin spectral sequence by degrees, and the the non collapse in other cases corresponds to familiar geometric behaviour.
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BibTeX
@misc{greenlees2026rational,
title = {{Rational torus equivariant spectra VII: the Cousin complex}},
author = {J. P. C. Greenlees},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23164},
eprint = {2610.23164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23164},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rational torus equivariant spectra VII: the Cousin complex
AU - J. P. C. Greenlees
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23164
UR - https://arxiv.org/abs/2610.23164
AB - We explore the analogy between rational G-spectra for an r-torus G and sheaves over an r-dimensional scheme, in the context of the author's algebraic model for rational G-spectra. In particular, the resolution of the sphere of a virtual representation in the standard model corresponds precisely to the Cousin complex resolution of a line bundle. The tom Dieck splitting for the sphere of an actual respresentation corresponds to the collapse of the Cousin spectral sequence by degrees, and the the non collapse in other cases corresponds to familiar geometric behaviour.
ER -