Endomorphisms of symbolic algebraic varieties
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.
regular selfmapping of a complex algebraic variety
scientific article; zbMATH DE number 1294431