When does an affine curve have an algebraic integer point?
Glasgow mathematical journal, Tome 26 (1985), pp. 1-4
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The purpose of this note is to draw attention to the question in the title. If C⊆Kn is an (absolutely) irreducible affine curve, defined by equations over a number field K, an algebraic integer point of C is a point P = (x1, ..., xn) with all of x1, ..., xn integers of some finite extension L of K. For such an algebraic integer point P to exist, there are obviously necessary local conditions: for every prime p of K there must exist a prime B above p and a corresponding finite extension LB of the completion Kp such that C has a B-adic integer point. We would like to know whether these obviously necessary local conditions are also sufficient.
Birch, B. J. When does an affine curve have an algebraic integer point?. Glasgow mathematical journal, Tome 26 (1985), pp. 1-4. doi: 10.1017/S0017089500006017
@article{10_1017_S0017089500006017,
author = {Birch, B. J.},
title = {When does an affine curve have an algebraic integer point?},
journal = {Glasgow mathematical journal},
pages = {1--4},
year = {1985},
volume = {26},
doi = {10.1017/S0017089500006017},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006017/}
}
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