• Corpus ID: 231639047

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

@inproceedings{Viehmann2021OnNS,
  title={On Newton strata in the \$B\_\{dR\}^+\$-Grassmannian},
  author={Eva Viehmann},
  year={2021}
}
We study parabolic reductions and Newton points of G-bundles on the Fargues-Fontaine curve and the Newton stratification on the B dR -Grassmannian for any reductive group G. Let BunG 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 BunG with Kottwitz’s set B(G), the closure relations on |BunG| coincide with the opposite of the usual partial order on B(G). Furthermore, we prove that every non-Hodge-Newton… 
5 Citations

Figures from this paper

A Harder-Narasimhan stratification of the $\B+$-Grassmannian
We establish a Harder-Narasimhan formalism for modifications of G-bundles on the Fargues-Fontaine curve. The semi-stable stratum of the associated stratification of the B dR -Grassmannian coincides
A JACOBIAN CRITERION FOR ARTIN v-STACKS
We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve [FS21, Section IV.4]. Namely, we
Compatibility of the Fargues-Scholze and Gan-Takeda Local Langlands
Given a prime p, a finite extension L/Qp, a connected p-adic reductive group G/L, and a smooth irreducible representation π of G(L), Fargues-Scholze [FS21] recently attached a semisimple Weil
The categorical form of Fargues' conjecture for tori
We prove the main conjecture of [FS21] for integral coefficients in the case of tori. Along the way we prove that the spectral action as constructed in that manuscript is compatible with the action
The Langlands program and the moduli of bundles on the curve
This is a review of the work of the authors on the geometrization of the local Langlands correspondence. We explain the geometry of the stack BunG of G-bundles on the curve, the structure of the

References

SHOWING 1-10 OF 40 REFERENCES
Minimal Newton Strata in Iwahori Double Cosets
  • E. Viehmann
  • Mathematics
    International Mathematics Research Notices
  • 2019
The set of Newton strata in a given Iwahori double coset in the loop group of a reductive group $G$ is indexed by a finite subset of the set $B(G)$ of Frobenius-conjugacy classes. For unramified
Fully Hodge–Newton Decomposable Shimura Varieties
The motivation for this paper is the study of arithmetic properties of Shimura varieties, in particular the Newton stratification of the special fiber of a suitable integral model at a prime with
Harder-Narasimhan strata and $p$-adic period domains
We revisit the Harder-Narasimhan stratification on a minuscule $p$-adic flag variety, by the theory of modifications of $G$-bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan
Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for any tamely ramified group $G$ and its parahoric subgroup
Geometric Langlands duality and representations of algebraic groups over commutative rings
As such, it can be viewed as a first step in the geometric Langlands program. The connected complex reductive groups have a combinatorial classification by their root data. In the root datum the
Relative P-adic Hodge Theory: Foundations
We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give
On the Hodge-Newton decomposition for split groups
The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazur's inequality for
The Harder–Narasimhan stratification of the moduli stack of $$G$$G-bundles via Drinfeld’s compactifications
We use Drinfeld’s relative compactifications $${\overline{\mathop {{\mathrm{Bun}}}\nolimits }}_P$$Bun¯P and the Tannakian viewpoint on principal bundles to construct the Harder–Narasimhan
Etale cohomology of diamonds
Motivated by problems on the etale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a
Berkeley Lectures on p-adic Geometry
This book presents an important breakthrough in arithmetic geometry. In 2014, this book's author delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory
...
...