Geometrization of the local Langlands correspondence
L Fargues, P Scholze - arXiv preprint arXiv:2102.13459, 2021 - arxiv.org
Following the idea of [Far16], we develop the foundations of the geometric Langlands
program on the Fargues--Fontaine curve. In particular, we define a category of $\ell $-adic …
program on the Fargues--Fontaine curve. In particular, we define a category of $\ell $-adic …
[HTML][HTML] Constructible sheaves on schemes
T Hemo, T Richarz, J Scholbach - Advances in Mathematics, 2023 - Elsevier
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients
in topological or even condensed rings. This is accomplished by defining lisse sheaves to …
in topological or even condensed rings. This is accomplished by defining lisse sheaves to …
On the -adic theory of local models
We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local
models of local Shimura varieties and the test function conjecture of Haines--Kottwitz in this …
models of local Shimura varieties and the test function conjecture of Haines--Kottwitz in this …
6-Functor Formalisms and Smooth Representations
C Heyer, L Mann - arXiv preprint arXiv:2410.13038, 2024 - arxiv.org
The purpose of this article is threefold: Firstly, we propose some enhancements to the
existing definition of 6-functor formalisms. Secondly, we systematically study the category of …
existing definition of 6-functor formalisms. Secondly, we systematically study the category of …
Meromorphic vector bundles on the Fargues--Fontaine curve
I Gleason, AB Ivanov - arXiv preprint arXiv:2307.00887, 2023 - arxiv.org
We introduce and study the stack of\textit {meromorphic} $ G $-bundles on the Fargues--
Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak …
Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak …
The singular support of an ℓ-adic sheaf
O Barrett - Tunisian Journal of Mathematics, 2024 - msp.org
The singular support of an -adic sheaf Page 1 Tunisian Journal of Mathematics an
international publication organized by the Tunisian Mathematical Society msp The singular …
international publication organized by the Tunisian Mathematical Society msp The singular …
On the Nori and Hodge realisations of Voevodsky\'etale motives
S Tubach - arXiv preprint arXiv:2309.11999, 2023 - arxiv.org
We show that the derived category of perverse Nori motives and mixed Hodge modules are
the derived categories of their constructible hearts. This enables us to construct $\infty …
the derived categories of their constructible hearts. This enables us to construct $\infty …
Modular functoriality in the local Langlands correspondence
T Feng - arXiv preprint arXiv:2312.12542, 2023 - arxiv.org
We develop a theory of Smith-Treumann localization and relative parity sheaves in the
context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We …
context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We …
Character Sheaves on Reductive Lie Algebras in Positive Characteristic
T Zhou - International Mathematics Research Notices, 2024 - academic.oup.com
We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over
an algebraically closed field of sufficiently large positive characteristic: a perverse …
an algebraically closed field of sufficiently large positive characteristic: a perverse …
Nonabelian Hodge isomorphisms for stacks and cohomological Hall algebras
L Hennecart - arXiv preprint arXiv:2307.09920, 2023 - arxiv.org
In this paper, we complete the nonabelian Hodge theory triangle of isomorphisms for stacks
between the Borel-Moore homologies of the Dolbeault, Betti and de Rham moduli stacks …
between the Borel-Moore homologies of the Dolbeault, Betti and de Rham moduli stacks …