Birth of Word, Synthesis of Meaning and Dimension of New Word / 8 September 2013

TANAKA Akio

Tokyo

8 September 2013

1.

The image lm(δX) of Map δ_χ  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 X that is finite type on Z≥0 and integer 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 i and j are regular closed immersion of codimension c,d. 

i:X→Y, j:Y→Z

Here is  given Cartesian diagram of the next scheme.

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

At this time the next equality sign is set up.

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

♦

If additional meaning be defined by the upper i 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.

[Reference]

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