Endomorphisms of symbolic algebraic varieties
type: Item
instance of: scholarly article
title: Endomorphisms of symbolic algebraic varieties
zbMATH Open document ID: 0998.14001
DOI: 10.1007/PL00011162
published in: Journal of the European Mathematical Society (JEMS)
publication date: 1999-06-02T00:00:00Z
review text: Summary: The theorem of \textit{J. Ax} [Ann. Math. (2) 88, 239-271 (1968; Zbl 0195.05701)] says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and is investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory, algebraic geometry, and symbolic dynamics.
Mathematics Subject Classification ID: 14A10
Mathematics Subject Classification ID: 37K20
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 1294431
zbMATH Keywords: regular selfmapping of a complex algebraic variety
zbMATH Keywords: surjunctivity
zbMATH Keywords: proregular mappings
zbMATH Keywords: proalgebraic spaces
zbMATH Keywords: proalgebraic varieties
zbMATH Keywords: model theory
zbMATH Keywords: symbolic dynamics
Wikidata QID: Q56474283
MaRDI profile type: Publication
cites work: The elementary theory of finite fields
cites work: Injective endomorphisms of varieties and schemes
cites work: Injective Morphisms of Real Algebraic Varieties
cites work: Injective endomorphisms of algebraic varieties
cites work: Q5669966
cites work: Q5562332
full work available at URL: pl00011162
OpenAlex ID: W2061789246
author: Misha Gromov
description: scientific article; zbMATH DE number 1294431