PreprintarXiv licencearXiv
RO(G)-graded cohomology of a point is self-injective
Abstract
Generalizing known results for G=C2 and constant underlineđť”˝2-coefficients, we show the RO(G)-graded Bredon cohomology of a point with constant underlinek-coefficients is self-injective whenever G is a finite subgroup of SO(3) and k is a finite field. Self-injectivity holds more generally for the RO(G)-graded homotopy of the Eilenberg--MacLane spectrum associated to a k-linear commutative Green functor M, whenever the spectrum HM is Anderson self-dual.
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BibTeX
@misc{hogle2026roggraded,
title = {{$RO(G)$-graded cohomology of a point is self-injective}},
author = {Eric Hogle and Clover May and Foling Zou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35351},
eprint = {2610.35351},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35351},
}
RIS
TY - UNPB
TI - RO(G)-graded cohomology of a point is self-injective
AU - Eric Hogle
AU - Clover May
AU - Foling Zou
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35351
UR - https://arxiv.org/abs/2610.35351
AB - Generalizing known results for G=C_2 and constant underlineđť”˝_2-coefficients, we show the RO(G)-graded Bredon cohomology of a point with constant underlinek-coefficients is self-injective whenever G is a finite subgroup of SO(3) and k is a finite field. Self-injectivity holds more generally for the RO(G)-graded homotopy of the Eilenberg--MacLane spectrum associated to a k-linear commutative Green functor M, whenever the spectrum HM is Anderson self-dual.
ER -