Diophantine Relations between Rings of $S$-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic
Shlapentokh, Alexandra
J. Symbolic Logic, Tome 58 (1993) no. 1, p. 158-192 / Harvested from Project Euclid
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One of the main theorems of the paper states the following. Let $R-K-M$ be finite extensions of a rational one variable function field $R$ over a finite field of constants. Let $S$ be a finite set of valuations of $K$. Then the ring of elements of $K$ having no poles outside $S$ has a Diophantine definition over its integral closure in $M$.
Publié le : 1993-03-14
Classification:  
@article{1183744183,
     author = {Shlapentokh, Alexandra},
     title = {Diophantine Relations between Rings of $S$-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic},
     journal = {J. Symbolic Logic},
     volume = {58},
     number = {1},
     year = {1993},
     pages = { 158-192},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744183}
}

Shlapentokh, Alexandra. Diophantine Relations between Rings of $S$-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic. J. Symbolic Logic, Tome 58 (1993) no. 1, pp.  158-192. http://gdmltest.u-ga.fr/item/1183744183/