An ind-Banach framework defines overconvergent and holomorphic power series rings to endow C-algebras with analytic structures, yielding an abstract GAGA-type comparison.
Condensed Mathematics and Complex Geometry
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
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 to make our general approach to analytic geometry via condensed mathematics more concrete by concentrating on the case of complex-analytic geometry. Instead of trying to develop new kinds of geometry, here we only try to redevelop the classical theory from a different point of view. More precisely, we reprove some important theorems for compact complex manifolds, including finiteness of coherent cohomology, Serre duality, GAGA and (Grothendieck--)Hirzebruch--Riemann--Roch.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Constructs a new zeta function via Berkovich motives that agrees with the classical congruence zeta function.
citing papers explorer
-
Analytification for Complex Geometry Revisited
An ind-Banach framework defines overconvergent and holomorphic power series rings to endow C-algebras with analytic structures, yielding an abstract GAGA-type comparison.