PreprintCC BY 4.0arXiv
Essential quotients of the cohomology of products of symmetric and alternating groups
Abstract
We calculate the quotient of the mod-two cohomology of a product of symmetric and alternating groups by the ideal of negligible elements, namely those that restrict trivially to any order-two subgroup. This quotient arises in the study of cohomological invariants of fields, as by work of Serre the ideal of negligible elements coincides with the ideal of elements that pull back trivially in Galois cohomology. Our calculations answer questions recently posed to us by J-P. Serre, whose recent results we build on. It is a pleasure to share these results on the occasion of his 100th birthday.
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BibTeX
@misc{hunter2026essential,
title = {{Essential quotients of the cohomology of products of symmetric and alternating groups}},
author = {Dana Hunter and Dev Sinha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14781},
eprint = {2609.14781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14781},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Essential quotients of the cohomology of products of symmetric and alternating groups
AU - Dana Hunter
AU - Dev Sinha
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14781
UR - https://arxiv.org/abs/2609.14781
AB - We calculate the quotient of the mod-two cohomology of a product of symmetric and alternating groups by the ideal of negligible elements, namely those that restrict trivially to any order-two subgroup. This quotient arises in the study of cohomological invariants of fields, as by work of Serre the ideal of negligible elements coincides with the ideal of elements that pull back trivially in Galois cohomology. Our calculations answer questions recently posed to us by J-P. Serre, whose recent results we build on. It is a pleasure to share these results on the occasion of his 100th birthday.
ER -