On Newton strata in the BdR+-Grassmannian

Abstract

We study parabolic reductions and Newton points of G-bundles on the Fargues–Fontaine curve and the Newton stratification on the $B_{\mathrm{dR}}^{+}$-Grassmannian for any reductive group G. Let ${\mathrm{Bun}}_G$ be the stack of G-bundles on the Fargues–Fontaine curve. Our first main result is to show that under the identification of the points of ${\mathrm{Bun}}_G$ with Kottwitz’s set $B(G)$, the closure relations on $|{\mathrm{Bun}}_G|$ coincide with the opposite of the usual partial order on $B(G)$. Furthermore, we prove that every non-Hodge–Newton decomposable Newton stratum in a minuscule affine Schubert cell in the $B_{\mathrm{dR}}^{+}$-Grassmannian intersects the weakly admissible locus, proving a conjecture of Chen. On the way, we study several interesting properties of parabolic reductions of G-bundles, and we determine which Newton strata have classical points.