Proceedings of the Japan Academy, Series A. Mathematical Sciences | |
The structure of Deitmar schemes, I | |
article | |
Koen Thas1  | |
[1] Ghent University, Department of Mathematics | |
关键词: Field with one element; Deitmar scheme; loose graph; automorphism group.; | |
DOI : 10.3792/pjaa.90.21 | |
学科分类:数学(综合) | |
来源: Japan Academy | |
【 摘 要 】
We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, $\mathbf{F}_{1}$) 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 $\mathbf{F}_{1}$ (such as combinatorial $\mathbf{F}_{1}$-projective and $\mathbf{F}_{1}$-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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300000399ZK.pdf | 106KB | download |