Line bundles on moduli spaces/stacks of G-bundles were studied intensively in 90’s by many mathematicians including Beauville, Laszlo, Sorger, Faltings, Kumar, Narasimhan, Teleman, etc. The main problems are the Verlinde formula for the dimension of global sections of these line bundles, and the determination of the Picard groups of the moduli spaces/stack of G-bundles.

In this talk, I will discuss some results on the same problems for the line bundles on the moduli stack of bundles over parahoric Bruhat-Tits group schemes over curves. These questions for parahoric bundles were first proposed by Pappas-Rapoport, and they generalize the classical story of parabolic bundles. This talk will be based on my previous work with Shrawan Kumar, and an ongoing joint work with Chiara Damiolini.