English

Stacks of p-adic shtukas and spatial kimberlites

Algebraic Geometry 2026-01-07 v1

Abstract

The main purpose of this article is to show that the special Newton polygon map from the stack of p-adic shtukas to the stack of G-bundles on the Fargues--Fontaine curve is representable in diamonds and sufficiently nice for cohomological considerations (i.e. fdcs). The second purpose is to show that the Fˉp\bar{\mathbb{F}}_p-fibers of the special Newton polygon map behave like formal schemes, and in particular, satisfy henselianity properties with respect to their reduced locus. These two goals achieved in this article are two of the crucial ingredients used in our collaboration with Hamman, Ivanov, Louren\c{c}o and Zou to construct the equivalence that compares the schematic and analytic local Langlands categories of Zhu and of Fargues--Scholze. To achieve these goals, we introduce and study spatial kimberlites, which is a better behaved variant of the theory previously developed by the author.

Keywords

Cite

@article{arxiv.2601.02741,
  title  = {Stacks of p-adic shtukas and spatial kimberlites},
  author = {Ian Gleason},
  journal= {arXiv preprint arXiv:2601.02741},
  year   = {2026}
}

Comments

49 pages. Comments are welcome