A defect relation for non-Archimedean analytic curves in arbitrary projective varieties

An, Ta

doi:10.1090/S0002-9939-06-08591-1

A defect relation for non-Archimedean analytic curves in arbitrary projective varieties
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by Ta Thi Hoai An PDF

Proc. Amer. Math. Soc. 135 (2007), 1255-1261 Request permission

Abstract:

If $f$ is a non-Archimedean analytic curve in a projective variety $X$ embedded in $\mathbb P^N$ and if $D_1,\dots ,D_q$ are hypersurfaces of $\mathbb P^N$ in general position with $X,$ then we prove the defect relation: \[ \sum _{j=1}^q \delta (f,D_j) \le \dim X. \]

References

Cherry, W., Hyperbolic $p$-adic analytic spaces, Ph.D. thesis, Yale University, 1993.
William Cherry and Zhuan Ye, Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem, Trans. Amer. Math. Soc. 349 (1997), no. 12, 5043–5071. MR 1407485, DOI 10.1090/S0002-9947-97-01874-6
Evertse, J.-H. and Ferretti R. G., A generalization of the Subspace Theorem with polynomials of higher degree, Preprint arXiv:math.NT/0408381.
Pei-Chu Hu and Chung-Chun Yang, Meromorphic functions over non-Archimedean fields, Mathematics and its Applications, vol. 522, Kluwer Academic Publishers, Dordrecht, 2000. MR 1794326, DOI 10.1007/978-94-015-9415-8
Serge Lang, Number theory. III, Encyclopaedia of Mathematical Sciences, vol. 60, Springer-Verlag, Berlin, 1991. Diophantine geometry. MR 1112552, DOI 10.1007/978-3-642-58227-1
Min Ru, A note on $p$-adic Nevanlinna theory, Proc. Amer. Math. Soc. 129 (2001), no. 5, 1263–1269. MR 1712881, DOI 10.1090/S0002-9939-00-05680-X
B. L. van der Waerden, Algebra. Vol. I, Springer-Verlag, New York, 1991. Based in part on lectures by E. Artin and E. Noether; Translated from the seventh German edition by Fred Blum and John R. Schulenberger. MR 1080172, DOI 10.1007/978-1-4612-4420-2