＜重要転載＞
https://rio2016.5ch.io/test/read.cgi/math/1717983856/725-726
関数論←複素関数論、な
2026/05/13
Condensed Mathematics and Complex Geometry
Dustin Clausen, Peter Scholze

とうとう出たか

https://people.mpim-bonn.mpg.de/scholze/
Prof. Dr. Peter Scholze
https://people.mpim-bonn.mpg.de/scholze/papers.html#Notes
Lecture Notes
Condensed Mathematics and Complex Geometry, lecture notes for course SS 22.

https://people.mpim-bonn.mpg.de/scholze/Complex.pdf
Condensed Mathematics and Complex Geometry
Dustin Clausen, Peter Scholze

Preface
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. Many thanks go to Ko Aoki and Mohan Ramachandran for many comments, and in particular for many pointers to the literature. Dustin Clausen and Peter Scholze May 2026

1. Lecture I: Introduction
Over the last few years, we have been working on an alternative foundation for the development of a (very general) “analytic geometry”, based on a new foundation for combining algebra and topology, in the framework of “condensed mathematics”. These ideas have been laid out in the lectures [Sch19] and [Sch20], given in 2019–2020. The goal of this course will be to make these developments more concrete by concentrating on the case of complex-analytic geometry, and instead of trying to develop new kinds of geometry, we will here merely try to redevelop the classical theory, but from a different point of view. More precisely, we aim to reprove some important theorems for compact complex manifolds, including:
(1) Finiteness of coherent cohomology;
(2) Serre Duality;
(3) In the algebraic case, GAGA;
(4) (Grothendieck–)Hirzebruch–Riemann–Roch.
The proofs will be very different from previous proofs.
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https://arxiv.org/abs/2605.11731
Mathematics > Complex Variables
[Submitted on 12 May 2026]
Condensed Mathematics and Complex Geometry
Dustin Clausen, Peter Scholze

https://en.wikipedia.org/wiki/Condensed_mathematics
Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which replaces a topological space by a certain sheaf of sets, in order to solve some technical problems of doing homological algebra on topological groups.

According to some,[who?] the theory aims to unify various mathematical subfields, including topology, complex geometry, and algebraic geometry.[citation needed] In particular, Kiran Kedlaya described condensed mathematics as "technology for doing commutative algebra over topological rings."[1]
Idea
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