对称群与交错群乘积上同调的essential商
Essential quotients of the cohomology of products of symmetric and alternating groups
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中文总结 AI 辅助
本文计算对称群与交错群乘积的模二上同调关于可忽略元素的商，回答Serre提出的问题，并基于其近期结果，用于域的上同调不变量研究。
中文摘要 AI 辅助
我们计算了对称群与交错群乘积的模二上同调关于可忽略元素理想的商，这些可忽略元素是指限制到任何二阶子群上均为平凡的元素。该商出现在域的上同调不变量的研究中，因为根据Serre的工作，可忽略元素理想与在伽罗瓦上同调中平凡拉回的元素理想一致。我们的计算回答了J-P. Serre最近向我们提出的问题，我们的工作建立在他近期的结果之上。在他百岁生日之际，我们很高兴分享这些结果。
英文摘要
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.
