Higher Pushforwards in Rigid Cohomology via Motives

Learn about Berthelot's conjecture and its connection to rigid cohomology through this mathematical lecture exploring how motivic non-archimedean homotopy theory provides new insights into overconvergent F-isocrystals. Discover the theoretical framework behind higher push-forwards in rigid cohomology of structure sheaves along smooth and proper morphisms, with particular focus on their canonical overconvergent properties. Explore the innovative approach using solid relative rigid cohomology to establish a proof of Berthelot's conjecture, demonstrating the powerful intersection of motivic homotopy theory and rigid analytic geometry. Gain understanding of advanced concepts in algebraic geometry and arithmetic geometry, including the technical machinery of F-isocrystals and their role in modern cohomological methods. The presentation covers joint research findings that advance our understanding of rigid cohomology theory and its applications in contemporary mathematical research.