ON NEWTON STRATA IN THE B_dR^C -GRASSMANNIAN

We study parabolic reductions and Newton points of G-bundles on the Fargues–Fontaine curve and the Newton stratification on the B_dR^C -Grassmannian for any reductive group G. Let 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 Bun_G with Kottwitz’s set B.G/, the closure relations on jBun_Gj 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_dR^C -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.