Geodesic
Witt vectors and the field with one element
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 146-159

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Witt vectors for Durov's generalized rings are constructed. The ring of Witt vectors for the field with one element is calculated. A criterion for the projectivity of modules over the residue field at archimedian point is given. This residue field is compared with the semiring of characteristic 1 in a construction of Connes and Consani. 
@article{ZNSL_2019_479_a7,
     author = {A. L. Smirnov},
     title = {Witt vectors and the field with one element},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--159},
     publisher = {mathdoc},
     volume = {479},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_479_a7/}
}
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A. L. Smirnov. Witt vectors and the field with one element. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 146-159. http://geodesic.mathdoc.fr/item/ZNSL_2019_479_a7/