@article{b66d07f303da46cfab35a43a9e7b6e01,
title = "Undecidability in function fields of positive characteristic",
abstract = "We prove that the first-order theory of any function field K of characteristic p > 2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.",
author = "Kirsten Eisentr{\"a}ger and Alexandra Shlapentokh",
note = "Funding Information: The authors would like to thank Arno Fehm and Stephen Simpson for helpful discussions leading to Corollary 5.1. The authors would also like to thank the referee for numerous corrections and helpful comments. K. Eisentr{\"a}ger was partially supported by NSF grant DMS-0801123 and a grant from the John Templeton Foundation. A. Shlapentokh was partially supported by NSF grants DMS-0354907 and DMS-0650927 as well as by a grant from the John Templeton Foundation.",
year = "2009",
doi = "10.1093/imrn/rnp079",
language = "English (US)",
volume = "2009",
pages = "4051--4086",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "21",
}