Endomorphisms of symbolic algebraic varieties

1999/06/30 by Misha Gromov · 5 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Cellular Automata and Applications #semigroups and automata theory #Mathematics #Endomorphism #Pure mathematics #Algebraic number #Algebra over a field #Algebraic variety #Dimension of an algebraic variety #Mathematical analysis

paper · pdf · doi:10.1007/pl00011162

openalex publication_date 1999/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and 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.

Citations

• Some general dynamical notions
• Endomorphisms and automorphisms of the shift dynamical system
• The Elementary Theory of Finite Fields

Cited by

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• On the injective self-maps of algebraic varieties
• Amenable groups and cellular automata
• Characteristic measures of symbolic dynamical systems
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• Garden of Eden (cellular automaton) [wikipedia]