Gluing sheaves along Harder-Narasimhan strata of ${\mathrm{Bun}}_G$

Abstract

We describe how to glue prime-to-$p$ torsion sheaves along Harder-Narasimhan strata of Fargues-Scholze's ${\mathrm{Bun}}_G$ in terms of the cohomology of locally closed strata inside the smooth charts ${\mathcal{M}}_b\to {\mathrm{Bun}}_G$ constructed in [FS21], which are moduli of certain split parabolic bundles. Our computations for $G={\mathrm{GL}}_2$ explicitly describe images of geometric constant term functors when restricted to a distinguished point inside ${\mathrm{Bun}}_{T_{\{b\}}}$, where $T_{\{b\}}$ is the split inner form of the Levi quotient of the corresponding parabolic subgroup $P_b$.

56 pages