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Watch a lecture from the 2024 Graduate Summer School Program on Motivic Homotopy Theory where Professor Markus Spitzweck from the University of Osnabrueck explores representation categories and motives. Delve into the theoretical foundations of mixed motives over fields with rational coefficients, examining their Tannakian properties and relationship to affine group scheme representations. Learn about recent developments in unconditional descriptions of motivic subcategories, including joint work with Heine that extends Iwanari's findings on derived representation categories from general linear groups to orthogonal and symplectic groups. Gain insights into how these extensions apply to motivic categories generated by principally polarized abelian schemes. The lecture is part of a comprehensive program featuring expert-led minicourses on various aspects of motivic homotopy theory, including its applications in algebra, algebraic geometry, and classical homotopy theory generalization.
