Arithmetic Geometry Language (2012 edition)
|
Dimension of Word
is morphism between regular arithmetic varieties.
is pullback.
.
#Here ends the paper.
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.
are morphism between regular arithmetic varieties, the next is concluded. .
2.
Interpretation of the upper theorem.
Word : 
.
.
Decomposition of word : 
, named pullback.
, named pullback.
Decomposed meaning unit in word : 
and 
.
and .
3.
Pullback is defined by the next from Efton Park, Complex Topologicak K-Theory, 2008.
Let 
and 
be topological spaces, let 
be avector bundle over 
, and suppose 
is a continuous map,
and be topological spaces, let be avector bundle over , and suppose is a continuous map,
Define
4.
Interpretation of theupper 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.
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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