On Newton strata in the B_{dR}^+-Grassmannian.

Viehmann, Eva

Abstract

We study parabolic reductions and Newton points of G-bundles on the Fargues–Fontaine curve and the Newton stratification on the B+dR𝐵dR+-Grassmannian for any reductive group G. Let BunGBun𝐺 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 BunGBun𝐺 with Kottwitz’s set B(G)𝐵(𝐺), the closure relations on |BunG||Bun𝐺| coincide with the opposite of the usual partial order on B(G)𝐵(𝐺). Furthermore, we prove that every non-Hodge–Newton decomposable Newton stratum in a minuscule affine Schubert cell in the B+dR𝐵dR+-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.