The structure of Deitmar schemes, I
 Author
 Koen Thas (UGent)
 Organization
 Abstract
 We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F1) to a socalled "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 F1 (such as combinatorial F1projective and F1affine 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.
 Keywords
 Deitmar scheme, Field with one element, loose graph, automorphism group, ZETAFUNCTIONS, F1
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU7184092
 Chicago
 Thas, Koen. 2014. “The Structure of Deitmar Schemes, I.” Proceedings of the Japan Academy Series Amathematical Sciences 90 (1): 21–26.
 APA
 Thas, K. (2014). The structure of Deitmar schemes, I. PROCEEDINGS OF THE JAPAN ACADEMY SERIES AMATHEMATICAL SCIENCES, 90(1), 21–26.
 Vancouver
 1.Thas K. The structure of Deitmar schemes, I. PROCEEDINGS OF THE JAPAN ACADEMY SERIES AMATHEMATICAL SCIENCES. 2014;90(1):21–6.
 MLA
 Thas, Koen. “The Structure of Deitmar Schemes, I.” PROCEEDINGS OF THE JAPAN ACADEMY SERIES AMATHEMATICAL SCIENCES 90.1 (2014): 21–26. Print.
@article{7184092, abstract = {We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F1) to a socalled {\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 F1 (such as combinatorial F1projective and F1affine 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 = {03862194}, journal = {PROCEEDINGS OF THE JAPAN ACADEMY SERIES AMATHEMATICAL SCIENCES}, keyword = {Deitmar scheme,Field with one element,loose graph,automorphism group,ZETAFUNCTIONS,F1}, language = {eng}, number = {1}, pages = {2126}, title = {The structure of Deitmar schemes, I}, volume = {90}, year = {2014}, }