Residues and Trace Maps in Grothendieck Duality - Lecture 4

Explore the fourth lecture in a series on Grothendieck Duality, focusing on residues and trace maps. Delve into advanced topics in algebraic geometry and commutative algebra as part of the "Dualities in Topology and Algebra" program. Gain insights from expert Suresh Nayak during this 1 hour 40 minute session, organized by the International Centre for Theoretical Sciences. Examine the connections between algebraic topology, commutative algebra, and modular representation theory of finite groups. Investigate duality phenomena and classification problems in tensor-triangulated categories. Discover how concepts from commutative algebra and algebraic geometry have been successfully applied to modular representation theory and stable homotopy category. Learn about Grothendieck duality theory, Gorenstein rings and schemes, and their generalizations of classical Poincaré duality for manifolds. Explore the classification of thick and localising subcategories of triangulated categories and the computation of their spectra. Enhance your understanding of cohomological support varieties and their development in modular representation theory.