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N. Durov Phd thesis "New Approach to Arakelov Geometry" is ofted mentioned as a beautiful approach to Arakelov geometry and it includes also a treatment of $\mathbb F_1$. It is a very long and technical text (>500 pages) and I read just the introduction.

Why I cannot find any follow up of this (unpublished) work? Is there any mistakes I am not aware of? Is there a lack of applications? Or maybe simply very few people were able to understand it...

It surprises me that this thesis is often mentioned in a positive manner but at the same time almost forgotten

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    $\begingroup$ This question would be improved if you included some links to where the thesis has been mentioned. $\endgroup$
    – Stopple
    Commented Jul 15, 2023 at 18:07
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    $\begingroup$ why "almost forgotten" ? the arXiv paper [ arxiv.org/abs/0704.2030 ] has been cited 125 times (Google Scholar); the author has many other interests [en.wikipedia.org/wiki/Nikolai_Durov], and only a few publications, but that by itself should be no reason to dismiss the thesis. $\endgroup$
    – Carlo Beenakker
    Commented Jul 15, 2023 at 18:23
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    $\begingroup$ I took the liberty to rephrase the title in a less offensive way. $\endgroup$
    – Carlo Beenakker
    Commented Jul 15, 2023 at 18:25
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    $\begingroup$ My gut feeling about many approaches to $\mathbb{F}_1$ is that they are technically correct (in the sense that the theorems follow from the definitions by the proofs), and I have no reason to doubt this of Durov's thesis in particular, but on the other hand none of the approaches is “right” in the sense that “this is not the $\mathbb{F}_1$ we are looking for”, i.e., they don't capture the properties which are expected or hoped of $\mathbb{F}_1$. But maybe this is like chasing unicorns. $\endgroup$
    – Gro-Tsen
    Commented Jul 15, 2023 at 19:05
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    $\begingroup$ This is the definition of a classic: everybody mentions it, but no one ever reads it. $\endgroup$
    – user473423
    Commented Jul 16, 2023 at 13:42

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