Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic

A. Shlapentokh

Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VIII, Tome 304 (2003), pp. 141-167

Résumé

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 $ML$.

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