Shi-Zhang Li

Poincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systems

We prove finiteness and Poincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systems on proper $p$-adic rigid-analytic spaces in the framework of Banach--Colmez spaces and establish their optimal cohomological vanishing bounds. As a consequence, we also obtain ordinary finiteness and duality for their arithmetic pro...