arXiv subjects

Sebastian Bartling

Publications and source records attributed to Sebastian Bartling.

7 recordsLinked to original sources

arXiv2026

Parahoric motivic Hecke categories in equal and mixed characteristic

We study constructible $\mathbb{Z}[\tfrac{1}{p}]$-linear \'etale motives on parahoric Hecke stacks associated with quasi-split tamely ramified reductive groups. We prove a canonical equivalence between their equal-characteristic and Witt-vector incarnations that is monoidal with respect to convolution. This extends Bando's comparison, which concerns split reductive groups and constructible \'etale sheaves. The proof combines the study of a family of affine Grassmannians for Pappas--Zhu group schemes with the use of the motivic nearby cycles functor.

math.AG↗

arXiv2026

Close fields, affine Springer fibers and fundamental lemmas

We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these families, and both the base change fundamental lemma and the standard endoscopic fundamental lemma transfer from characteristic zero to arbitrary positive characteristic.

math.NT↗

arXiv2024

Vanishing of Brauer groups of moduli stacks of stable curves

We show that the cohomological Brauer groups of the moduli stacks of stable genus $g$ curves over the integers and an algebraic closure of the rational numbers vanish for any $g\geq 2$. For the $n$ marked version, we show the same vanishing result in the range $(g,n)=(1,n)$ with $1\leq n \leq 6$ and all $(g,n)$ with $g\geq 4.$ We also discuss several finiteness results on cohomological Brauer groups of proper and smooth Deligne-Mumford stacks over the integers.

math.AG↗

arXiv2024

Moduli spaces of nilpotent displays

We show that the moduli problem of deformations of nilpotent displays by quasi-isogenies is representable, without using $p$-divisible groups. The main ingredients are Artin's criterion and the theory of truncated displays. This gives in particular a new proof for the representability of Rapoport-Zink spaces.

math.AG↗

arXiv2022

Sur la cohomologie étale de la courbe de Fargues-Fontaine

In this article the étale cohomology of constructible torsion sheaves on the étale site of the algebraic resp. adic Fargues-Fontaine curve is analyzed. In the $\ell\neq p$-torsion case, two conjectures of Fargues are verified: vanishing in degrees greater than two and the comparison between the étale cohomology of the adic and the algebraic curve. In the $p$-torsion case, under a certain assumption, the vanishing of the étale cohomology in degrees greater than two of those Zariski-constructible sheaves on the adic curve that come via pullback from the algebraic curve is proven.

math.AG↗

arXiv2022

$\mathcal{G}$-$μ$-displays and local shtuka

Two approaches to the construction of integral models of local Shimura-varieties are compared: that of Bültel-Pappas using $\mathcal{G}$-$μ$-displays and that of Scholze using local mixed-characteristic shtuka. As an application, the representability of the diamond of the generic fiber of the Bültel-Pappas moduli problem is verified and a local representability conjecture of Rapoport-Pappas is proven. The methods apply to all unramified local Shimura-data under a certain condition on slopes and if $p\neq 2;$ thus in particular also to exceptional groups.

math.NT↗

arXiv2022

The universal special formal $\mathcal{O}_{D}$-module for $d=2$

A new proof of an old theorem of Drinfeld concerning the representability of the moduli problem of special formal $\mathcal{O}_{D}$-modules by Deligne's $p$-adic formal model of Drinfeld's upper half-plane is given for $d=2.$ The display associated to the universal object is constructed explicitly.

math.NT↗