Dimension of Word
TANAKA Akio
24 December 2012
24 December 2012
1.
Theorem by C. Soulé, Lectures on Arakelov Geometry, 1992.
is morphism between regular arithmetic varieties.
is pullback.
When are morphism between regular arithmetic varieties, the next is concluded.
.
2.
Interpretation of the upper theorem.
Word : .
Decomposition of word : , named pullback.
Decomposed meaning unit in word : and .
3.
Pullback is defined by the next from Efton Park, Complex Topological K-Theory, 2008.
Let and be topological spaces, let be a vector bundle over , and suppose is a continuous map,
Define
4.
Interpretation of the upper theorem 2.
Word can be deposed to meaning units by pullback.
Meaning unit also become pullback.
5.
Pullback contains order function ord.
ord contains length.
Here length is longitude of composition series.
Here composition series is defined by the next.
A is commutative ring.
M is A module.
If A be field, is M's dimension over A.
6.
From 5. leads the next supposition.
When word is decomposed to meaning unit, each unit has dimension that determines word's dimension.
(Here ends the paper.)
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