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Explore the Motivic Action Conjecture through the lens of Doi-Naganuma lifts in this advanced number theory lecture from the Institute for Advanced Study. Delve into the surprising property of cohomology in locally symmetric spaces where Hecke operators act on multiple cohomological degrees with identical eigenvalues. Examine Venkatesh and collaborators' proposed arithmetic explanation involving a hidden degree-shifting action of motivic cohomology groups. Learn about the conjecture's setup for coherent cohomology of Hilbert modular forms over â„‚ and discover recent supporting results from collaborative research with Alex Horawa. This joint IAS/Princeton University Number Theory seminar provides deep insights into the intersection of algebraic number theory, motivic cohomology, and modular forms, making it essential viewing for researchers and advanced students working in arithmetic geometry and related fields.
