Cohomology of Arithmetic Groups and Integral Structures on Automorphic Representations

Explore the deep connections between cohomology of arithmetic groups and integral structures on automorphic representations in this mathematical lecture. Delve into the construction of rational and integral structures on spaces of automorphic forms of reductive groups, examining how these structures emerge from the cohomology of arithmetic groups. Learn about the fundamental concept of locally algebraic representations and discover how they generate locally algebraic g,K-modules and associated sheaves on arithmetic orbifolds. Understand how these advanced mathematical frameworks address conceptual challenges in the standard treatment of arithmetic groups and their cohomology, while aligning with Langlands' philosophical approach to parametrizing L-functions through L-group representations. Gain insights into how these theoretical developments contribute to the broader understanding of automorphic forms and their applications in modern number theory and representation theory.