This is a very soft and speculative question. Please feel free to downvote, close or delete it.

Studying the cohomology of moduli spaces of shtukas, Drinfeld proved the Langlands program for $\mathrm{GL}_2$ for global function fields, which was later extended by L. Lafforgue to $\mathrm{GL}_n$.

Peter Scholze has a conjectural section **Shtukas for $\mathrm{Spec}\,\mathbf{Z}$** in his 2018 ICM report https://arxiv.org/abs/1712.03708 on arXiv.

Might this be used to attack the Langlands conjectures for $\mathbf{Q}$ (and how)?

What could this be used for?

mightbe possible to construct a cohomology theory for arithmetic schemes, that should morally be motivic in nature, but concrete and workable, in the meantime that all the conjectures on algebraic cycles remain untouched $\endgroup$ – user87684 Jan 11 '18 at 7:313more comments