Nagoya Mathematical Journal

Algebraic dependence of meromorphic mappings in value distribution theory

Yoshihiro Aihara

Full-text: Open access


In this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space $X$ over the complex $m$-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of $X$. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve $E$ and give conditions under which two holomorphic mappings from $X$ into $E$ are algebraically related.

Article information

Nagoya Math. J., Volume 169 (2003), 145-178.

First available in Project Euclid: 27 April 2005

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}
Secondary: 32H04: Meromorphic mappings


Aihara, Yoshihiro. Algebraic dependence of meromorphic mappings in value distribution theory. Nagoya Math. J. 169 (2003), 145--178.

Export citation


  • G. Cornell, Exponential growth of the $l$-rank of the class group of the maximal real subfield of cyclotomic fields , Bull. Amer. Math. Soc., 8 (1983), 55--58.
  • G. Cornell and M. Rosen, The $l$-rank of the real class group of cyclotomic fields , Compositio Math., 53 (1984), 133--141.
  • R. Greenberg, On the structure of certain Galois groups , Invent. Math., 47 (1978), 85--99.
  • K. Iwasawa, On $\boldZ_l$-extensions of algebraic number fields , Ann. of Math., 98 (1973), 246--326.
  • J.C. Lagarias and A.M. Odlyzko, Effective version of the Chebotarev density theorem , Algebraic number fields, (Durham Symposium, 1975; ed. by A.Fröhlich), Academic Press, London, 1977, 409--464.
  • F. Lemmermeyer, Ideal class groups of cyclotomic number fields II , Acta. Arith., 84 (1998), 59--70.
  • M. Ozaki, The class group of $\Z_p$-extensions over totally real number fields , Tôhoku Math. J., 49 (1997), 431-435.
  • L.C. Washington, Introduction to Cyclotomic Fields (2nd. edition), Graduate Texts in Math. 83, Springer-Verlag, New York (1997).
  • A. Wiles, The Iwasawa conjecture for totally real fields , Ann. of Math., 131 (1990), 493--540.