Geodesic
Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field
Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 2103-2138.

Voir la notice de l'article provenant de la source EMS Press

We prove that the existential theory of any function field K of characteristic p>0 is undecidable in the language of rings augmented by constant symbols for the elements of a suitable recursive subfield, provided that the constant field does not contain the algebraic closure of a finite field. This theorem is the natural generalization of a theorem of Kim and Roush from 1992. We also extend our previous undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of any function field of positive characteristic is undecidable in the language of rings without parameters.
DOI : 10.4171/jems/714
Classification : 11-XX, 03-XX
Keywords: Undecidability, Hilbert's Tenth Problem 
@article{JEMS_2017_19_7_a5,
     author = {Kirsten Eisentr\"ager and Alexandra Shlapentokh},
     title = {Hilbert's {Tenth} {Problem} over function fields of positive characteristic not containing the algebraic closure of a finite field},
     journal = {Journal of the European Mathematical Society},
     pages = {2103--2138},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2017},
     doi = {10.4171/jems/714},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/714/}
}
TY  - JOUR
AU  - Kirsten Eisenträger
AU  - Alexandra Shlapentokh
TI  - Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 2103
EP  - 2138
VL  - 19
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/714/
DO  - 10.4171/jems/714
ID  - JEMS_2017_19_7_a5
ER  - 
%0 Journal Article
%A Kirsten Eisenträger
%A Alexandra Shlapentokh
%T Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field
%J Journal of the European Mathematical Society
%D 2017
%P 2103-2138
%V 19
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/714/
%R 10.4171/jems/714
%F JEMS_2017_19_7_a5
Kirsten Eisenträger; Alexandra Shlapentokh. Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field. Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 2103-2138. doi : 10.4171/jems/714. http://geodesic.mathdoc.fr/articles/10.4171/jems/714/

Cité par Sources :