Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hunter, Dana, Sinha, Dev
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213256055