| Résume | The cohomology groups of proetale $\mathbf{Q}_p$-local systems on rigid-analytic varieties over $\mathbf{C}_p$ can be infinite-dimensional $\mathbf{Q}_p$-vector spaces even when the varieties are smooth and proper. Nevertheless, a recent result of Anschuetz-Le Bras-Mann shows that in the smooth and proper case they still have the structure of Banach-Colmez spaces and satisfy a version of Poincare duality. In my talk, I will discuss some background for this statement and then explain a different proof, which is essentially diagrammatic and follows a similar strategy as a previous argument in the case of $\mathbf{F}_p$-local systems. Joint work in progress with Shizhang Li, Wieslawa Niziol and Bogdan Zavyalov. |
