Monday 12 June 2023

Dimension Conjecture at Synthesis of Meaning

 

Dimension Conjecture at Synthesis of Meaning


TANAKA Akio

Tokyo
9 September 2013

1.
The image lm(δX) of Map δχ  is expressed by Zr(X)rat .
Here the next Chow group of r-cycle is defined.
CHr(X):=Zr(X)/Zr(X)rat .

<Birth of New Word>
Bass conjecture
For scheme that is finite type on Z≥0 and intger r≥o, CHr(X) is finite generative Abel group.
If language be the upper X, word is defined by  CHr(X) that is finite generative.

2.
<Synthesis of Meaning>

Transition theorem
The next and are regular closed immersion of codimension c,d

i:XYj:YZ

Here is  given Cartesian diagram of the next scheme.

X'i'Y' j'→Z'
↓          ↓          ↓
X— i j → Z

At this time the next equality sign is set up.

(j O i)! = i! O j! : CHr(Z') → CHr–c–d(X')

If additional meaning be defined by the upper and j, there is synthesis of meaning. 

3.

<Dimension of New Word>

If word be defined by CHr(X) and additional meaning is defined by i and j, the dimension of new word  is deduced from old word's r to r-c-d.

4.

<Dimension Conjecture at Synthesis of Meaning>

When word synthesises meaning, word reduces own dimension according to codimension of additional meaning.


[Reference]

-On dimension

-OnTransition theorem

  • W. Fulton. Intersection Theory. Berlin, Springer. 1988.

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