Abstract
We relate the integrability of vector fields, and of the vanishing of $p$-torsion, to model-theoretic questions concerning separably closed fields, endowed canonically with a derivation. While each differential field $(F_p(t)^s,D_p)$ is known to be decidable, we show that the asymptotic theory of these fields as a class is undecidable in a strong sense. This precludes a geometric answer to certain generalizations of the Grothendieck-Katz conjecture.
Citation
Zoé Chatzidakis. Ehud Hrushovski. "Asymptotic theories of differential fields." Illinois J. Math. 47 (3) 593 - 618, Fall 2003. https://doi.org/10.1215/ijm/1258138183
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