5 papers
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…