hillseverzoho / Arithmetic Geometry Language / Dimension Conjecture at Synthesis of Meaning

 

Home /  hillseverhome / hillseverzoho / Dimension Conjecture      at Synthesis of Meaning Dimension Conjecture at Synthesis of Meaning TANAKA Akio Tokyo 9 September 2013 hillseversunlit 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 X 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 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! : CHr(Z') → CHr–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. 4. <Dimension Conjecture at Synthesis of Meaning> When word synthesises meaning, word reduces own dimension according to codimension of additional meaning. [Reference] -On dimension Dimension of Word / 30 January 2012 / serkinanlum True-false problem of the Crete / 22 July 2013 / atbankofdamzoho -OnTransition theorem W. Fulton. Intersection Theory. Berlin, Springer. 1988.