### The structure of Deitmar schemes, I

(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:
http://hdl.handle.net/1854/LU-7184092

- author
- Koen Thas UGent
- organization
- year
- 2014
- 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.