Lang Model

Lang Model

TANAKA Akio

1. Lang conjecture (S.Lang 1974)
Algebraic field F ( finite dimensional overfield over Q ) is defined over projective algebraic variety V.
For a certain embedding F -> C, V is seen that V is seen as complex projective algebraic variety.
If V is Kobayashi hyperbolic, V ( F ) is finite set.

2. Shafarevich conjecture ( I.Shafarevich 1963)
F is algebraic field.
O_F is integer ring of F.
Finite subset  and integer  are fixed.
When the upper conditions are satisfied, g dimensional Abelian variety over F and genius g's algebraic curves that degenerate in only S at most only exist finite number.

3. Interpretation
3.1 Finiteness of words by Shafarevich conjecture
Language := FSentence := O_FWord := SWord's dimension := gWord's meaning := genius g's algebraic curves 3.2 Grammar (Connection of words) by Lang conjecture
Language := FGrammar (Words' connection rule) := Kobayashi hyperbolicity

4. References
4.1 On dimension and meaning
Quantum Theory for Language 2004
4.2 On Kobayashi hyperbolicity
Ditance Theory 2004
From Distance to Pseudo-Kobayashi-Distance 2012

This paper's description is unfinished.

Tokyo

17 June 2012

Sekinan Research Field of Language