Illinois Journal of Mathematics

Uniqueness theorem for non-Archimedean analytic curves intersecting hyperplanes without counting multiplicities

Qiming Yan

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Abstract

In this paper, we prove uniqueness theorems for analytic curves from $\mathbf{F}$ to ${\mathbb{P}}^{n}(\mathbf{F})$ sharing hyperplanes in general position without counting multiplicities, where $\mathbf{F}$ is a complete algebraically closed non-Archimedean field of arbitrary characteristic.

Article information

Source
Illinois J. Math., Volume 55, Number 4 (2011), 1657-1668.

Dates
First available in Project Euclid: 12 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1373636700

Digital Object Identifier
doi:10.1215/ijm/1373636700

Mathematical Reviews number (MathSciNet)
MR3082885

Zentralblatt MATH identifier
1320.32030

Subjects
Primary: 11J99: None of the above, but in this section 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}

Citation

Yan, Qiming. Uniqueness theorem for non-Archimedean analytic curves intersecting hyperplanes without counting multiplicities. Illinois J. Math. 55 (2011), no. 4, 1657--1668. doi:10.1215/ijm/1373636700. https://projecteuclid.org/euclid.ijm/1373636700


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References

  • W. W. Adams and E. G. Straus, Non-archimedean analytic functions taking the same values at the same points, Illinois J. Math. 15 (1971), 418–424.
  • W. Cherry and C. Toropu, Generalized ABC theorems for non-Archimedean entire functions of several vaiables in arbitrary characteristic, Acta Arith. 136 (2009), 351–384.
  • L.-C. Hsia and J. T.-Y. Wang, The ABC theorem for higher-dimensional function fields, Trans. Amer. Math. Soc. 356 (2004), 2871–2887.
  • R. Nevanlinna, Einige eindeutigkeitssätze in der theorie der meromorphen funktionen, Acta Math. 48 (1926), 367–391.
  • M. Ru, Uniqueness theorems for $p$-adic holomorphic curves, Illinois J. Math. 45 (2001), 487–493.