# Endomorphisms of symbolic algebraic varieties

Journal of the European Mathematical Society (1999)

- Volume: 001, Issue: 2, page 109-197
- ISSN: 1435-9855

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topGromov, 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 -

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