I will describe the objects one obtains by descent from $G$-bundles on a tame Galois cover of a given curve, answering a question raised by Grothendieck in his Bourbaki talk in 1956 on Weil's "memoire paper" from 1938. Joint work with George Pappas.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/faltings70