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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 523, Pages 159–165 (Mi znsl7350)  
On Gauss' rings and Deuring's argument

A. L. Smirnov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
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Abstract: The Dedekind rings multiplicativly indistinguishable with $\mathbb{Z}$ are classified. Certain inaccuracies of a previous paper are corrected. Deuring's reasoning related to the Riemann conjecture and the finiteness of the list of Gauss’ class number problem for imaginary quadratic 10-th discriminant problem are heuvristically explained.
Key words and phrases: generalized ring, Durov's approach, field with one element, noncommutative tensor square, field with class number one, Riemann conjecture.
Received: 23.10.2023
Document Type: Article
UDC: 511.2
Language: Russian
Citation: A. L. Smirnov, “On Gauss' rings and Deuring's argument”, Algebra and number theory. Part 6, Zap. Nauchn. Sem. POMI, 523, POMI, St. Petersburg, 2023, 159–165
Citation in format AMSBIB
\Bibitem{Smi23}
\by A.~L.~Smirnov
\paper On Gauss' rings and Deuring's argument
\inbook Algebra and number theory. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 523
\pages 159--165
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7350}
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