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When does an affine curve have an algebraic integer point?

Published online by Cambridge University Press:  18 May 2009

B. J. Birch
B. J. Birch
Affiliation:
Mathematical Institute, 24–29 St. Giles', Oxford, OX1 3LB
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 1 - 4
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

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