Formal functions on homogeneous spaces
type: Item
instance of: scholarly article
title: Formal functions on homogeneous spaces
zbMATH Open document ID: 0615.14029
DOI: 10.1007/BF01391497
author: Wei-Liang Chow
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143389
review text: The author generalizes one of his previous theorems: Suppose \(X=G/H\) is an algebraic variety (over a field), homogeneous under a connected algebraic group G. Suppose further that \(Y\subseteq X\) is a subvariety generating G, that is (if Y contains the origin) the connected component of 1 of the preimage of Y in G generates G. Under these assumptions any formal meromorphic function on the formal completion of X along Y is algebraic. The proof uses rigid analytic methods, but in fact Grothendieck's algebraisation for formal schemes suffices. The key is the behaviour under formal completion of the K/k-span of the variety: If \(K\supseteq k\) is a field extension, X a variety defined over k, and \(Y\subseteq X_ K\) a K-subvariety, its K/k-span is defined to be the smallest k-subvariety of X containing Y. In a previous result [Ann. Math., II. Ser. 89, 391-403 (1969; Zbl 0184.465)] the author considered complex analytic meromorphic functions.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14A99
zbMATH DE Number: 3995877
zbMATH Keywords: homogeneous algebraic variety
zbMATH Keywords: formal meromorphic function
zbMATH Keywords: formal completion
MaRDI profile type: Publication
cites work: On meromorphic maps of algebraic varieties
cites work: On the Algebraicity of Certain Ringed Spaces
cites work: Formale Geometrie und homogene Räume
cites work: Q5594277
cites work: Q5735274
reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 3995877