Lang Model
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.
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.
OF 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.
F is algebraic field.
OF 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 := F
Sentence := OF
Word := SWord's dimension := g
Word's meaning := genius g's algebraic curves
3.2 Grammar (Connection of words) by Lang conjecture
Language := F
Grammar (Words' connection rule) := Kobayashi hyperbolicity
3.1 Finiteness of words by Shafarevich conjecture
Language := F
Sentence := OF
Word := SWord's dimension := g
Word's meaning := genius g's algebraic curves
3.2 Grammar (Connection of words) by Lang conjecture
Language := F
Grammar (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
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
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