Poincaré duality for \(p\)-adic Lie groups (Q616140)

In this paper the following Poincaré duality theorem is proven: Let \(G\) be a \(p\)-adic group of dimension \(d\) and \(V\) be a finite dimensional \(\mathbb Q_p\)-vector space with a continuous action of \(G\). Let \(\check{V} = \Hom_{\mathbb Q_p}(V,D_{\mathbb Q_p})\) be its dual. Then the natural cup-product pairing \[ \langle .,.\rangle: H^i(G,V) \times H^{d-i}(G,\check{V}) \to H^d(G,D_{\mathbb Q_p}) \cong \mathbb Q_p \] is perfect. (Theorem 1.1).