6 papers
Analytic de Rham stacks of Fargues-Fontaine curves
Johannes Anschütz, Guido Bosco, Arthur-César Le Bras +2
We define and initiate the study of analytic de Rham stacks of relative Fargues-Fontaine curves. To this end, we develop a theory of analytic de Rham stacks with sufficiently stron…
Wild Betti sheaves
Peter Scholze
In this note, we consider the problem of constructing an enlargement of the category of Betti sheaves that supports an ``exponential local system'' on , and a Fourier eq…
Geometrization of the local Langlands correspondence, motivically
Peter Scholze
Based on the formalism of rigid-analytic motives of Ayoub--Gallauer--Vezzani, we extend our previous work with Fargues from -adic sheaves to motivic sheaves. In particular, w…
Berkovich Motives
Peter Scholze
We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean s…
Geometric Eisenstein series I: finiteness theorems
Linus Hamann, David Hansen, Peter Scholze
We develop the theory of geometric Eisenstein series and constant term functors for -adic sheaves on stacks of bundles on the Fargues-Fontaine curve. In particular, we prove…
The Local Langlands correspondence for $\GL_n$ over -adic fields
Peter Scholze
We reprove the Local Langlands Correspondence for $\GL_n$ over -adic fields as well as the existence of -adic Galois representations attached to (most) regular algebraic c…