Explore a mathematical lecture that delves into a relative version of mod-p Poincare duality for proper morphism of rigid-analytic varieties over p-adic fields. Learn about novel trace map constructions for smooth and proper morphisms of rigid-analytic varieties, while following a diagrammatic proof approach to mod-p Poincare duality. Developed in collaboration with Shizhang Li and Bogdan Zavyalov, this advanced mathematics presentation from Institut des Hautes Etudes Scientifiques (IHES) provides deep insights into non-archimedean geometry and its theoretical foundations.