Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VIII, Tome 304 (2003), pp. 141-167
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Let $M$ be a field of positive characteristic $p>0$ such that $C$, the closure of a finite field in $M$, has an extension of degree $p$. Let $L$ be a field finitely generated over $C$ and such that $M$ and $L$ are linearly disjoint over $C$. Then Hilbert's Tenth problem is not decidable over $ML$.
@article{ZNSL_2003_304_a8,
author = {A. Shlapentokh},
title = {Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {141--167},
publisher = {mathdoc},
volume = {304},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_304_a8/}
}
TY - JOUR AU - A. Shlapentokh TI - Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic JO - Zapiski Nauchnykh Seminarov POMI PY - 2003 SP - 141 EP - 167 VL - 304 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2003_304_a8/ LA - ru ID - ZNSL_2003_304_a8 ER -
%0 Journal Article %A A. Shlapentokh %T Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic %J Zapiski Nauchnykh Seminarov POMI %D 2003 %P 141-167 %V 304 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2003_304_a8/ %G ru %F ZNSL_2003_304_a8
A. Shlapentokh. Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VIII, Tome 304 (2003), pp. 141-167. http://geodesic.mathdoc.fr/item/ZNSL_2003_304_a8/