Residues and Trace Maps in Grothendieck Duality - Lecture 3

Explore the intricacies of residues and trace maps in Grothendieck duality in this advanced mathematics lecture. Delve into the third installment of Suresh Nayak's series, presented as part of the "Dualities in Topology and Algebra" program at the International Centre for Theoretical Sciences. Gain insights into the connections between algebraic topology, commutative algebra, and modular representation theory of finite groups. Examine the derived category of commutative rings and its role as a model for stable categories in various mathematical fields. Investigate the application of Grothendieck duality theory and Gorenstein rings to algebraic topology, and discover how these concepts generalize classical Poincaré duality for manifolds. Enhance your understanding of thick and localising subcategories in triangulated categories, Balmer spectra computation, and cohomological support varieties. Suitable for those with a background in algebraic topology, commutative algebra, and homological algebra, this 1 hour and 29 minutes lecture offers a deep dive into advanced mathematical concepts within the broader context of duality phenomena in mathematics.