Dualizing complexes on the moduli of parabolic bundles

Abstract

For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on $\mathrm{Bun}_P$, the moduli stack of $P$-bundles on the Fargues--Fontaine curve, can be described explicitly in terms of the modulus character of $P$. As applications, we identify various characters appearing in the theory of local and global Shimura varieties, show the Harris--Viehmann conjecture in the Hodge--Newton reducible case, and carry out some computations of the geometric Eisenstein functors for general parabolics.