Diophantine Language Finiteness of Words

Home  »   Papers »  Diophantine Language »  Finiteness of Word Diophantine Language Finiteness of Words TANAKA Akio [Preparation 1] k is algebraic field.  is finite subset. V is projective algebraic manifold over k. D is defined divisor over k. All the sub-manifolds are over k. Rational point is k-rational point. [Preparation 2] L is rich line bundle. |L| is complete linear system. D is divisor of |L|.  is regular cut to D.  is approximate function to D.  is counting function to D.  is rich line bundle. When  islarge,  becomes rich.  is basis of  .  is embedding. [Definition 1]  ,  ,  . [Definition 2] Subset of rational points  \  is integer under the next condition. (i) There exists a certain constant  . (ii)  \  . [Theorem, Faltings] A is Abelian variety over k. When D is reduced rich divisor, arbitrary integer subset  \  is always finite set. [Interpretation] D is meaning minimum.  \  is word. A is language. [References] From Cell to Manifold / Cell Theory / Tokyo June 2, 2007 Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008 Language, Word, Distance, Meaning and Meaning Minimum by Riemann-Roch Formula / Tokyo August 15, 2009 Tokyo January 29Sekinan Research Field of Languag e