Vector Bundle Model by Grothemdieck's Theorem/ For SAEKI Shizuto and our youth days / 6 January 2012

Vector Bundle Model by Grothendieck's Theorem

For SAEKI Shizuto and our youth days

TANAKA Akio

Pⁿ is projective space.
P¹ is projective line.
E is vector bundle over P¹.

Theorem (Grothendieck)
Vector bundle E over projective line P¹ is isomorphic with direct sum of line bundles.

[Note 1]
Language is supposed to be projective space Pⁿ.
Word is supposed to be projective line P¹.
Meaning of word is supposed to be vector bundle E over projective line P¹.
Under the upper suppositions, by theorem (Grothendieck) meaning is identified with direct sum of line bundles.

[Note 2]
X is algebraic manifold.
O^X is module over X.
L is easy sheaf of O^X.
Line bundle satisfies the following at L.
(i) Stalk L_μ at generating point is one-dimensional vector space over functional field k(X).
(ii) L is locally isomorphic with structural sheaf O_X .

[Note 3]
(Replacement (i)) One-dimensional vector space over functional field k(X) is replaced to r-dimentional.
(Replacement (ii)) Locally structural sheaf O_X is replaced to to .
Replacement (i) and (ii) is called vector bundle of rank r or locally free sheaf.

[Note 4]
Language universal model is expressed by .

[Reference]
Vector bundle model is a description of the next paper of Aurora Theory.
Dictoron and Aurora < Language is aurora dancing above us> For SAEKI Shizuto. Tokyo, September24, 2006.

Tokyo
January 6, 2012
Sekinan Research Field of Language

[Reference added, January 10, 2012]
The Time of Language