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Explore cellular A1-homology, a groundbreaking homology theory for smooth algebraic varieties over perfect fields, in this 70-minute conference talk delivered at the Centre International de Rencontres Mathématiques. Delve into the fundamental concepts of cellular A1-homology and examine its role as the motivic counterpart to Poincaré duality in classical topology. Learn about specific conjectures regarding the cellular A1-homology of smooth projective varieties and understand their verification process for smooth projective rational surfaces. Based on collaborative research with Fabien Morel, this presentation was recorded during the thematic meeting "Motivic homotopy in interaction" in Marseille, France. Access this mathematical discourse through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched content with abstracts and bibliographies, and comprehensive search functionality for an enhanced learning experience.
