6 papers
Condensed Mathematics and Complex Geometry
Dustin Clausen, Peter Scholze
This is a slightly revised version of lectures notes for a course in Summer 2022 joint between Bonn and Copenhagen, intended as a stable citable version. The goal of this course is…
Lectures on Analytic Geometry
Peter Scholze
This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part o…
Six-Functor Formalisms
Peter Scholze
These are lecture notes for a course in Winter 2022/23, updated and completed in October 2025. The goal of the lectures is to present some recent developments around six-functor fo…
The Habiro ring of a number field
Stavros Garoufalidis, Peter Scholze, Campbell Wheeler +1
We introduce the Habiro ring of a number field and modules over it graded by . Elements of these modules are collections of power series at each compl…
A note on higher almost ring theory
Fabian Hebestreit, Peter Scholze
We explain a derived version of the basic construction of localisations of module categories by means of idempotent ideals, which lie at the heart of Faltings' almost ring theory.…
On topological cyclic homology
Thomas Nikolaus, Peter Scholze
Topological cyclic homology is a refinement of Connes--Tsygan's cyclic homology which was introduced by Bökstedt--Hsiang--Madsen in 1993 as an approximation to algebraic -theory…