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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Why I cannot find any follow up of this (unpublished) work?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

Carlo Beenakker
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    This question would be improved if you included some links to where the thesis has been mentioned. – Stopple Jul 15 '23 at 18:07
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    why "almost forgotten" ? the arXiv paper [ https://arxiv.org/abs/0704.2030 ] has been cited 125 times (Google Scholar); the author has many other interests [https://en.wikipedia.org/wiki/Nikolai_Durov], and only a few publications, but that by itself should be no reason to dismiss the thesis. – Carlo Beenakker Jul 15 '23 at 18:23
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    I took the liberty to rephrase the title in a less offensive way. – Carlo Beenakker Jul 15 '23 at 18:25
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    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. – Gro-Tsen Jul 15 '23 at 19:05
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    It is surprising to me that anything can be often mentioned but almost forgotten! – Geoffrey Irving Jul 15 '23 at 22:15
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    This is the definition of a classic: everybody mentions it, but no one ever reads it. –  Jul 16 '23 at 13:42
  • A related question has two answers which contain some possibly useful explanations. In short, there has been some interesting work but it's too soon to see if Durov's thesis will have remarkable applications. This was nearly 4 years ago, I am not sure whether things have changed in the meantime (I am not an expert of this field at all). At any rate, I think that we may exclude for sure that any mistake has been found. – Damiano Mazza Jul 21 '23 at 11:22

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