有限群的坚实对偶性
Solid Duality for Profinite Groups
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中文总结 AI 辅助
研究有限群同调与上同调间类似庞加莱对偶性，通过凝聚数学框架分类此类群，统一推广现有结果并构造新例，是利用该框架研究有限群（上）同调的首批工作之一。
中文摘要 AI 辅助
我们对在同调与上同调之间具有类似庞加莱对偶性的有限群进行分类。我们的证明适用于每个有限系数环，以及有限和离散系数。我们不仅统一和推广了现有结果，还构造了两个新的对偶群例子。我们通过凝聚数学框架证明结果。这一最近发展的背景是有限对象的自然归宿，我们的工作是首批利用此研究有限群（上）同调的工作之一。建立对偶结果涉及对凝聚数学中同调有限性性质的研究。
英文摘要
We classify profinite groups that have a Poincaré-like duality between their homology and cohomology. Our proofs work over every profinite coefficient ring, and for profinite as well as discrete coefficients. We do not only unify and generalise existing results, but also construct two novel examples of duality groups. We prove our results via the framework of condensed mathematics. This recently developed setting is a natural home for profinite objects, and our work is among the first to leverage this for the study of the (co)homology of profinite groups. Establishing our duality results involves an investigation of homological finiteness properties in condensed mathematics.
