J. P. Sorenson, ANTS-8 Poster Session Organizer [5] V. Goppa, Algebraico-Geometric codes, V. D. Goppa, Math USSR Izvestiya Vol. 21 (1983) No. 1 75-91. [6] R. Hartshorne, Algebraic geometry, Graduate texts in mathematics 52, Springer-Verlag, 1977. [7] J. W. P. Hirschfeld, Finite projective spaces of three dimensions, Clarendon press. Oxford 1985. [8] P. P. Spurr, Linear codes over GF (4). Master s Thesis, University of North Carolina at Chapell Hill, USA, 1986. [9] I. R. Shafarevich, Basic algebraic geometry 1, Springer-Verlag, 1994. [10] A. B. Sørensen, Rational points on hypersurfaces, Reed-Muller codes and algebraic-geometric codes. Ph. D. Thesis, Aarhus, Denmark, 1991. Curves of genus 2 with many rational points via K3 surfaces Noam D. Elkies, Harvard University, elkies@math.harvard.edu Let C be a (smooth, projective, absolutely irreducible) curve of genus g ¥ 2 over a number eld K. Faltings [Fa1, Fa2] proved that the set C(K) of K-rational points of C is nite, as conjectured by Mordell. The proof can even yield an e ective upper bound on the size #C(K) of this set (though not, in general, a provably complete list of points); but this bound depends on the arithmetic of C. This suggests the question of how
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Curves of genus 2 with many rational points via K3 surfaces (abstract only)
Elkies, Noam D.
Follow ACM Communications in Computer Algebra
, Volume 42 (1-2)
Association for Computing Machinery – Jul 25, 2008
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