Geodesic
Proof of the congruence conjecture for generalized rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 91-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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In 2007 A. L. Smirnov formulated an interesting conjecture on generalized rings introduced and studied by N. V. Durov. In this paper we prove the conjecture. 
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S. A. Evdokimov. Proof of the congruence conjecture for generalized rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 91-94. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a7/

[1] A. L. Smirnov, “Obobschënnye podkoltsa arifmeticheskikh kolets”, Zap. nauchn. semin. POMI, 349, 2007, 211–241 | MR

[2] N. Durov, New approach to Arakelov geometry, 16 Apr. 2007, arXiv: 0704.2030[math AG]