Endomorphisms of symbolic algebraic varieties

Gromov, Misha. "Endomorphisms of symbolic algebraic varieties." Journal of the European Mathematical Society 001.2 (1999): 109-197. <http://eudml.org/doc/277515>.

@article{Gromov1999,
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.},
author = {Gromov, Misha},
journal = {Journal of the European Mathematical Society},
keywords = {regular selfmapping of a complex algebraic variety; surjunctivity; proregular mappings; proalgebraic spaces; proalgebraic varieties; model theory; symbolic dynamics; regular selfmapping of a complex algebraic variety; surjunctivity; proregular mappings; proalgebraic spaces; proalgebraic varieties; model theory; symbolic dynamics},
language = {eng},
number = {2},
pages = {109-197},
publisher = {European Mathematical Society Publishing House},
title = {Endomorphisms of symbolic algebraic varieties},
url = {http://eudml.org/doc/277515},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Gromov, Misha
TI - Endomorphisms of symbolic algebraic varieties
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 2
SP - 109
EP - 197
AB - 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.
LA - eng
KW - regular selfmapping of a complex algebraic variety; surjunctivity; proregular mappings; proalgebraic spaces; proalgebraic varieties; model theory; symbolic dynamics; regular selfmapping of a complex algebraic variety; surjunctivity; proregular mappings; proalgebraic spaces; proalgebraic varieties; model theory; symbolic dynamics
UR - http://eudml.org/doc/277515
ER -