Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields

Explore local-global principles for homogeneous spaces over arithmetic function fields in this 58-minute conference talk by Julia Hartmann from the University of Pennsylvania. Delivered at AGNES 2023 at Stony Brook University, the presentation delves into the study of local-global principles for rational points on homogeneous spaces under linear algebraic groups. Focus on function fields of curves over complete discretely valued fields and examine various collections of overfields for analyzing local-global principles. Learn about the methods derived from patching and their connections to formal and rigid geometry. Gain insights into this collaborative research conducted with J.L.-Colliot-Thélène, D. Harbater, D. Krashen, R. Parimala, and V. Suresh, expanding on classical studies over number fields and function fields of curves over finite fields.