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The structure of Deitmar schemes, I

Koen Thas UGent (2014) PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES. 90(1). p.21-26
abstract
We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F-1) to a so-called "loose graph" (which is a generalization of a graph). Several properties of the Deitmar scheme can be proven easily from the combinatorics of the (loose) graph, and it also appears that known realizations of objects over F-1 (such as combinatorial F-1-projective and F-1-affine spaces) exactly depict the loose graph which corresponds to the associated Deitmar scheme. This idea is then conjecturally generalized so as to describe all Deitmar schemes in a similar synthetic manner.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Deitmar scheme, Field with one element, loose graph, automorphism group, ZETA-FUNCTIONS, F-1
journal title
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES
Proc. Jpn. Acad. Ser. A-Math. Sci.
volume
90
issue
1
pages
21 - 26
Web of Science type
Article
Web of Science id
000330486700005
JCR category
MATHEMATICS
JCR impact factor
0.221 (2014)
JCR rank
301/312 (2014)
JCR quartile
4 (2014)
ISSN
0386-2194
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7184092
handle
http://hdl.handle.net/1854/LU-7184092
date created
2016-04-14 13:15:13
date last changed
2018-06-13 11:02:44
@article{7184092,
  abstract     = {We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F-1) to a so-called {\textacutedbl}loose graph{\textacutedbl} (which is a generalization of a graph). Several properties of the Deitmar scheme can be proven easily from the combinatorics of the (loose) graph, and it also appears that known realizations of objects over F-1 (such as combinatorial F-1-projective and F-1-affine spaces) exactly depict the loose graph which corresponds to the associated Deitmar scheme. This idea is then conjecturally generalized so as to describe all Deitmar schemes in a similar synthetic manner.},
  author       = {Thas, Koen},
  issn         = {0386-2194},
  journal      = {PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES},
  keyword      = {Deitmar scheme,Field with one element,loose graph,automorphism group,ZETA-FUNCTIONS,F-1},
  language     = {eng},
  number       = {1},
  pages        = {21--26},
  title        = {The structure of Deitmar schemes, I},
  volume       = {90},
  year         = {2014},
}

Chicago
Thas, Koen. 2014. “The Structure of Deitmar Schemes, I.” Proceedings of the Japan Academy Series A-mathematical Sciences 90 (1): 21–26.
APA
Thas, K. (2014). The structure of Deitmar schemes, I. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 90(1), 21–26.
Vancouver
1.
Thas K. The structure of Deitmar schemes, I. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES. 2014;90(1):21–6.
MLA
Thas, Koen. “The Structure of Deitmar Schemes, I.” PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 90.1 (2014): 21–26. Print.