UBC Algebra and Algebraic Geometry Seminar: Emanuel Reinecke

While the etale cohomology of Z/p-local systems on smooth p-adic rigid spaces is in general hard to control, it becomes more tractable when the spaces are proper. For example, in the proper case it is finite-dimensional and has recently been shown in work of Zavyalov and of Mann to satisfy Poincare duality. In my talk, I will explain a new, essentially "diagrammatic" proof of Poincare duality in this context, which also works for more general spaces and coefficients and in the relative setting. The argument relies on a novel construction of trace maps for smooth morphisms of rigid spaces. Joint work with Shizhang Li and Bogdan Zavyalov.