On the strongly regular locus of the inertia stack of ${\mathrm{Bun}}_G$

Abstract

Let $G$ be a connected reductive group over a finite extension of ${\mathbb{Q}}_p$. We show that for each $b\in B(G)$, the strongly regular locus of the inertia stack of ${\mathrm{Bun}}_G^b$ is open in the inertia stack of ${\mathrm{Bun}}_G$. As a consequence, we extend the computation of Hansen--Kaletha--Weinstein of trace distributions of the cohomology of local shtuka spaces ${\mathrm{Sht}}_{G,b,\mu }$ to non-basic $b$. If $b$ is closed in $B(G,\mu )$, or $b$ is basic and has only one specialization in $B(G,\mu )$, then we compute the trace distribution of the entire strongly regular locus. In the process, we prove some results on the behavior of characteristic classes under cohomologically smooth pullback.

arXiv comment28 pages, fixed typos