72 citations · 221 across the 16 of their papers we have counts for
6 papers · 1 filter
Lectures on Condensed Mathematics
Peter Scholze
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint wor…
Prismatic -crystals and crystalline Galois representations
Bhargav Bhatt, Peter Scholze
Let be a complete discretely valued field of mixed characteristic with perfect residue field. We prove that the category of prismatic -crystals on is…
On the generic part of the cohomology of non-compact unitary Shimura varieties
Ana Caraiani, Peter Scholze
We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, exte…
Potential automorphy over CM fields
Patrick B. Allen, Frank Calegari, Ana Caraiani +7
Let be a CM number field. We prove modularity lifting theorems for regular -dimensional Galois representations over without any self-duality condition. We deduce that al…
On torsion in the cohomology of locally symmetric varieties
Peter Scholze
The main result of this paper is the existence of Galois representations associated with the mod (or mod ) cohomology of the locally symmetric spaces for $\GL_n$ over a to…
Moduli of p-divisible groups
Peter Scholze, Jared Weinstein
We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, a…